Unitary matrix

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my web-site; cheap psychic readings [netwk.hannam.ac.kr] The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems spontaneously evolve toward thermodynamic equilibrium—the state of maximum entropy. Equivalently, perpetual motion machines of the second kind are impossible.

The second law is an empirically validated postulate of thermodynamics, but it can be understood and explained using the underlying quantum statistical mechanics. In the language of statistical mechanics, entropy is a measure of the number of microscopic configurations corresponding to a macroscopic state. Because thermodynamic equilibrium corresponds to a vastly greater number of microscopic configurations than any non-equilibrium state, it has the maximum entropy, and the second law follows because random chance alone practically guarantees that the system will evolve towards such thermodynamic equilibrium.

It is an expression of the fact that over time, differences in temperature, pressure, and chemical potential decrease in an isolated non-gravitational physical system, leading eventually to a state of thermodynamic equilibrium.

The second law may be expressed in many specific ways, but the first formulation is credited to the French scientist Sadi Carnot in 1824 (see Timeline of thermodynamics). Strictly speaking, the early statements of the Second Law are only correct in a horizontal plane in a gravitational field.

The second law has been shown to be equivalent to the internal energy U being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, ...).

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Description

The first law of thermodynamics provides the basic definition of thermodynamic energy, also called internal energy, associated with all thermodynamic systems, but unknown in classical mechanics, and states the rule of conservation of energy in nature.

The concept of energy in the first law does not, however, account for the observation that natural processes have a preferred direction of progress. For example, heat always flows spontaneously from regions of higher temperature to regions of lower temperature, and never the reverse, unless external work is performed on the system. The first law is completely symmetrical with respect to the initial and final states of an evolving system. The key concept for the explanation of this phenomenon through the second law of thermodynamics is the definition of a new physical property, the entropy.

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$dS={\frac {\delta Q}{T}}\!$

The entropy of an isolated system in its own internal thermodynamic equilibrium does not change with time. An isolated system may consist initially of several subsystems, separated from one another by partitions, but still each in its own internal thermodynamic equilibrium. If the partitions are removed, the former subsystems will in general interact and produce a new common final system in its own internal thermodynamic equilibrium. The sum of the entropies of the initial subsystems is in general less than the entropy of the final common system. If all of the initial subsystems have all the same values of their intensive variables, then the sum of the initial entropies will be equal to the final common entropy, and the final common system will have the same values of its intensive variables.

For a body in thermal equilibrium with another, there are indefinitely many empirical temperature scales, in general respectively depending on the properties of a particular reference thermometric body. Thermal equilibrium between two bodies entails that they have equal temperatures. The zeroth law of thermodynamics in its usual short statement allows recognition that two bodies have the same temperature, especially that a test body has the same temperature as a reference thermometric body. The second law allows a distinguished temperature scale, which defines an absolute, thermodynamic temperature, independent of the properties of any particular thermometric body.

The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.

Carnot's principle

The historical origin of the second law of thermodynamics was in Carnot's principle. It refers to a cycle of a Carnot engine, fictively operated in the limiting mode of extreme slowness known as quasi-static, so that the heat and work transfers are between subsystems that are always in their own internal states of thermodynamic equilibrium. The Carnot engine is an idealized device of special interest to engineers who are concerned with the efficiency of heat engines. Carnot's principle was recognized by Carnot at a time when the caloric theory of heat was seriously considered, before the recognition of the first law of thermodynamics, and before the mathematical expression of the concept of entropy. Interpreted in the light of the first law, it is physically equivalent to the second law of thermodynamics, and remains valid today. It states

The efficiency of a quasi-static or reversible Carnot cycle depends only on the temperatures of the two heat reservoirs, and is independent of the working substance. A Carnot engine operated in this way is the most efficient possible heat engine using those two temperatures.

Clausius statement

The German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the Clausius statement:

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

Heat cannot spontaneously flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of refrigeration, for example. In a refrigerator, heat flows from cold to hot, but only when forced by an external agent, the refrigeration system.

Kelvin statement

Lord Kelvin expressed the second law as

It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

Planck's Principle

In 1926 Max Planck wrote an important paper on the basics of thermodynamics. He indicated the principle

The internal energy of a closed system is increased by an isochoric adiabatic process.

This formulation does not mention heat and does not mention temperature, nor even entropy, and does not necessarily implicitly rely on those concepts, but it implies the content of the second law. A closely related statement is that "Frictional pressure never does positive work." Using a now obsolete form of words, Planck himself wrote: "The production of heat by friction is irreversible."

Principle of Carathéodory

Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:

In every neighborhood of any state S of an adiabatically isolated system there are states inaccessible from S.

With this formulation he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, $\delta Q=TdS$.

Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.

Equivalence of the Clausius and the Kelvin statements

Derive Kelvin Statement from Clausius Statement

Suppose there is an engine violating the Kelvin statement: i.e.,one that drains heat and converts it completely into work in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the graph. The net and sole effect of this newly created engine consisting of the two engines mentioned is transferring heat $\Delta Q=Q\left({\frac {1}{\eta }}-1\right)$ from the cooler reservoir to the hotter one, which violates the Clausius statement. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.

Gravitational systems

In non-gravitational systems, objects always have positive heat capacity, meaning that the temperature rises with energy. Therefore, when energy flows from a high-temperature object to a low-temperature object, the source temperature is decreased while the sink temperature is increased; hence temperature differences tend to diminish over time.

However, this is not always the case for systems in which the gravitational force is important. The most striking examples are black holes, which - according to theory - have negative heat capacity. The larger the black hole, the more energy it contains, but the lower its temperature. Thus, the supermassive black hole in the center of the milky way is supposed to have a temperature of 10⁻¹⁴ K, much lower than the cosmic microwave background temperature of 2.7K, but as it absorbs photons of the cosmic microwave background its mass is increasing so that its low temperature further decreases with time.

For this reason, gravitational systems tend towards non-even distribution of mass and energy.

Corollaries

Perpetual motion of the second kind

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Before the establishment of the Second Law, many people who were interested in inventing a perpetual motion machine had tried to circumvent the restrictions of First Law of Thermodynamics by extracting the massive internal energy of the environment as the power of the machine. Such a machine is called a "perpetual motion machine of the second kind". The second law declared the impossibility of such machines.

Carnot theorem

Carnot's theorem (1824) is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs. Carnot's theorem states:

• All irreversible heat engines between two heat reservoirs are less efficient than a Carnot engine operating between the same reservoirs.
• All reversible heat engines between two heat reservoirs are equally efficient with a Carnot engine operating between the same reservoirs.

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot however further postulated that some caloric is lost, not being converted to mechanical work. Hence no real heat engine could realise the Carnot cycle's reversibility and was condemned to be less efficient.

Though formulated in terms of caloric (see the obsolete caloric theory), rather than entropy, this was an early insight into the second law.

Clausius Inequality

The Clausius Theorem (1854) states that in a cyclic process

$\oint {\frac {\delta Q}{T}}\leq 0.$

The equality holds in the reversible case and the '<' is in the irreversible case. The reversible case is used to introduce the state function entropy. This is because in cyclic processes the variation of a state function is zero from state functionality.

Thermodynamic temperature

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. For an arbitrary heat engine, the efficiency is:

$\eta ={\frac {A}{q_{H}}}={\frac {q_{H}-q_{C}}{q_{H}}}=1-{\frac {q_{C}}{q_{H}}}\qquad (1)$

where A is the work done per cycle. Thus the efficiency depends only on q_C/q_H.

Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, any reversible heat engine operating between temperatures T₁ and T₂ must have the same efficiency, that is to say, the efficiency is the function of temperatures only: ${\frac {q_{C}}{q_{H}}}=f(T_{H},T_{C})\qquad (2).$

In addition, a reversible heat engine operating between temperatures T₁ and T₃ must have the same efficiency as one consisting of two cycles, one between T₁ and another (intermediate) temperature T₂, and the second between T₂ andT₃. This can only be the case if

$f(T_{1},T_{3})={\frac {q_{3}}{q_{1}}}={\frac {q_{2}q_{3}}{q_{1}q_{2}}}=f(T_{1},T_{2})f(T_{2},T_{3}).$

Now consider the case where $T_{1}$ is a fixed reference temperature: the temperature of the triple point of water. Then for any T₂ and T₃,

$f(T_{2},T_{3})={\frac {f(T_{1},T_{3})}{f(T_{1},T_{2})}}={\frac {273.16\cdot f(T_{1},T_{3})}{273.16\cdot f(T_{1},T_{2})}}.$

Therefore if thermodynamic temperature is defined by

$T=273.16\cdot f(T_{1},T)\,$

then the function f, viewed as a function of thermodynamic temperature, is simply

$f(T_{2},T_{3})={\frac {T_{3}}{T_{2}}},$

and the reference temperature T₁ will have the value 273.16. (Of course any reference temperature and any positive numerical value could be used—the choice here corresponds to the Kelvin scale.)

Entropy

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. According to the Clausius equality, for a reversible process

$\oint {\frac {\delta Q}{T}}=0$

That means the line integral $\int _{L}{\frac {\delta Q}{T}}$ is path independent.

So we can define a state function S called entropy, which satisfies

$dS={\frac {\delta Q}{T}}\!$

With this we can only obtain the difference of entropy by integrating the above formula. To obtain the absolute value, we need the Third Law of Thermodynamics, which states that S=0 at absolute zero for perfect crystals.

For any irreversible process, since entropy is a state function, we can always connect the initial and terminal status with an imaginary reversible process and integrating on that path to calculate the difference in entropy.

Now reverse the reversible process and combine it with the said irreversible process. Applying Clausius inequality on this loop,

$-\Delta S+\int {\frac {\delta Q}{T}}=\oint {\frac {\delta Q}{T}}<0$

Thus,

$\Delta S\geq \int {\frac {\delta Q}{T}}\,\!$

where the equality holds if the transformation is reversible.

Notice that if the process is an adiabatic process, then $\delta Q=0$, so $\Delta S\geq 0$.

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Whatever changes to dS and dS_R occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy S_tot of the isolated total system must not decrease:

$dS_{\mathrm {tot} }=dS+dS_{R}\geq 0$

According to the First Law of Thermodynamics, the change dU in the internal energy of the sub-system is the sum of the heat δq added to the sub-system, less any work δw done by the sub-system, plus any net chemical energy entering the sub-system d ∑μ_iRN_i, so that:

$dU=\delta q-\delta w+d(\sum \mu _{iR}N_{i})\,$

where μ_iR are the chemical potentials of chemical species in the external surroundings.

Now the heat leaving the reservoir and entering the sub-system is

$\delta q=T_{R}(-dS_{R})\leq T_{R}dS$

where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the Second Law inequality from above.

It therefore follows that any net work δw done by the sub-system must obey

$\delta w\leq -dU+T_{R}dS+\sum \mu _{iR}dN_{i}\,$

It is useful to separate the work δw done by the subsystem into the useful work δw_u that can be done by the sub-system, over and beyond the work p_R dV done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done:

$\delta w_{u}\leq -d(U-T_{R}S+p_{R}V-\sum \mu _{iR}N_{i})\,$

It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or exergy E of the subsystem,

$E=U-T_{R}S+p_{R}V-\sum \mu _{iR}N_{i}$

The Second Law therefore implies that for any process which can be considered as divided simply into a subsystem, and an unlimited temperature and pressure reservoir with which it is in contact,

$dE+\delta w_{u}\leq 0\,$

i.e. the change in the subsystem's exergy plus the useful work done by the subsystem (or, the change in the subsystem's exergy less any work, additional to that done by the pressure reservoir, done on the system) must be less than or equal to zero.

In sum, if a proper infinite-reservoir-like reference state is chosen as the system surroundings in the real world, then the Second Law predicts a decrease in E for an irreversible process and no change for a reversible process.

$dS_{tot}\geq 0$ Is equivalent to $dE+\delta w_{u}\leq 0$

This expression together with the associated reference state permits a design engineer working at the macroscopic scale (above the thermodynamic limit) to utilize the Second Law without directly measuring or considering entropy change in a total isolated system. (Also, see process engineer). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found (See second law efficiency.)

This approach to the Second Law is widely utilized in engineering practice, environmental accounting, systems ecology, and other disciplines.

History

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Nicolas Léonard Sadi Carnot in the traditional uniform of a student of the École Polytechnique.

The first theory of the conversion of heat into mechanical work is due to Nicolas Léonard Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its environment.

Recognizing the significance of James Prescott Joule's work on the conservation of energy, Rudolf Clausius was the first to formulate the second law during 1850, in this form: heat does not flow spontaneously from cold to hot bodies. While common knowledge now, this was contrary to the caloric theory of heat popular at the time, which considered heat as a fluid. From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865).

Established during the 19th century, the Kelvin-Planck statement of the Second Law says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.

The ergodic hypothesis is also important for the Boltzmann approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.

It has been shown that not only classical systems but also quantum mechanical ones tend to maximize their entropy over time. Thus the second law follows, given initial conditions with low entropy. More precisely, it has been shown that the local von Neumann entropy is at its maximum value with a very high probability. The result is valid for a large class of isolated quantum systems (e.g. a gas in a container). While the full system is pure and therefore does not have any entropy, the entanglement between gas and container gives rise to an increase of the local entropy of the gas. This result is one of the most important achievements of quantum thermodynamics.To succeed in selling a home, it is advisable be competent in real estate advertising and marketing, authorized, monetary, operational aspects, and other information and skills. This is essential as a result of you want to negotiate with more and more sophisticated buyers. You could outperform rivals, use latest technologies, and stay ahead of the fast altering market.

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Today, much effort in the field is attempting to understand why the initial conditions early in the universe were those of low entropy, as this is seen as the origin of the second law (see below).

Informal descriptions

The second law can be stated in various succinct ways, including:

• It is impossible to produce work in the surroundings using a cyclic process connected to a single heat reservoir (Kelvin, 1851).
• It is impossible to carry out a cyclic process using an engine connected to two heat reservoirs that will have as its only effect the transfer of a quantity of heat from the low-temperature reservoir to the high-temperature reservoir (Clausius, 1854).
• If thermodynamic work is to be done at a finite rate, free energy must be expended. (Stoner, 2000)

Mathematical descriptions

Rudolf Clausius

In 1856, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form:

$\int {\frac {\delta Q}{T}}=-N$

where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:

The entropy of the universe tends to a maximum.

This statement is the best-known phrasing of the second law. Moreover, owing to the general broadness of the terminology used here, e.g. universe, as well as lack of specific conditions, e.g. open, closed, or isolated, to which this statement applies, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This, of course, is not true; this statement is only a simplified version of a more complex description.

In terms of time variation, the mathematical statement of the second law for an isolated system undergoing an arbitrary transformation is:

${\frac {dS}{dt}}\geq 0$

where

S is the entropy of the system and

t is time.

The equality sign holds in the case that only reversible processes take place inside the system. If irreversible processes take place (which is the case in real systems in operation) the >-sign holds. An alternative way of formulating of the second law for isolated systems is:

${\frac {dS}{dt}}={\dot {S}}_{i}$ with ${\dot {S}}_{i}\geq 0$

with ${\dot {S}}_{i}$ the sum of the rate of entropy production by all processes inside the system. The advantage of this formulation is that it shows the effect of the entropy production. The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines. Multiplied with ambient temperature $T_{a}$ it gives the so-called dissipated energy $P_{diss}=T_{a}{\dot {S}}_{i}$.

The expression of the second law for closed systems (so, allowing heat exchange and moving boundaries, but not exchange of matter) is:

${\frac {dS}{dt}}={\frac {\dot {Q}}{T}}+{\dot {S}}_{i}$ with ${\dot {S}}_{i}\geq 0$

Here

${\dot {Q}}$ is the heat flow into the system

$T$ is the temperature at the point where the heat enters the system.

If heat is supplied to the system at several places we have to take the algebraic sum of the corresponding terms.

For open systems (also allowing exchange of matter):

${\frac {dS}{dt}}={\frac {\dot {Q}}{T}}+{\dot {S}}+{\dot {S}}_{i}$ with ${\dot {S}}_{i}\geq 0$

Here ${\dot {S}}$ is the flow of entropy into the system associated with the flow of matter entering the system. It should not be confused with the time derivative of the entropy. If matter is supplied at several places we have to take the algebraic sum of these contributions.

Statistical mechanics gives an explanation for the second law by postulating that a material is composed of atoms and molecules which are in constant motion. A particular set of positions and velocities for each particle in the system is called a microstate of the system and because of the constant motion, the system is constantly changing its microstate. Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/√N where N is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical deviations from that predicted by the second law. Classical thermodynamic theory does not deal with these statistical variations.

Derivation from statistical mechanics

47 year-old Podiatrist Hyslop from Alert Bay, has lots of hobbies and interests that include fencing, property developers in condo new launch singapore and handball. Just had a family trip to Monasteries of Haghpat and Sanahin. Due to Loschmidt's paradox, derivations of the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the Big Bang), though other scenarios have also been suggested.

Given these assumptions, in statistical mechanics, the Second Law is not a postulate, rather it is a consequence of the fundamental postulate, also known as the equal prior probability postulate, so long as one is clear that simple probability arguments are applied only to the future, while for the past there are auxiliary sources of information which tell us that it was low entropy.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. The first part of the second law, which states that the entropy of a thermally isolated system can only increase is a trivial consequence of the equal prior probability postulate, if we restrict the notion of the entropy to systems in thermal equilibrium. The entropy of an isolated system in thermal equilibrium containing an amount of energy of $E$ is:

$S=k_{\mathrm {B} }\ln \left[\Omega \left(E\right)\right]\,$

where $\Omega \left(E\right)$ is the number of quantum states in a small interval between $E$ and $E+\delta E$. Here $\delta E$ is a macroscopically small energy interval that is kept fixed. Strictly speaking this means that the entropy depends on the choice of $\delta E$. However, in the thermodynamic limit (i.e. in the limit of infinitely large system size), the specific entropy (entropy per unit volume or per unit mass) does not depend on $\delta E$.

Suppose we have an isolated system whose macroscopic state is specified by a number of variables. These macroscopic variables can, e.g., refer to the total volume, the positions of pistons in the system, etc. Then $\Omega$ will depend on the values of these variables. If a variable is not fixed, (e.g. we do not clamp a piston in a certain position), then because all the accessible states are equally likely in equilibrium, the free variable in equilibrium will be such that $\Omega$ is maximized as that is the most probable situation in equilibrium.

If the variable was initially fixed to some value then upon release and when the new equilibrium has been reached, the fact the variable will adjust itself so that $\Omega$ is maximized, implies that the entropy will have increased or it will have stayed the same (if the value at which the variable was fixed happened to be the equilibrium value).

The entropy of a system that is not in equilibrium can be defined as:

$S=-k_{\mathrm {B} }\sum _{j}P_{j}\ln \left(P_{j}\right)$

see here. Here the $P_{j}$ is the probabilities for the system to be found in the states labeled by the subscript j. In thermal equilibrium, the probabilities for states inside the energy interval $\delta E$ are all equal to $1/\Omega$, and in that case the general definition coincides with the previous definition of S that applies to the case of thermal equilibrium.

Suppose we start from an equilibrium situation and we suddenly remove a constraint on a variable. Then right after we do this, there are a number $\Omega$ of accessible microstates, but equilibrium has not yet been reached, so the actual probabilities of the system being in some accessible state are not yet equal to the prior probability of $1/\Omega$. We have already seen that in the final equilibrium state, the entropy will have increased or have stayed the same relative to the previous equilibrium state. Boltzmann's H-theorem, however, proves that the entropy will increase continuously as a function of time during the intermediate out of equilibrium state.

Derivation of the entropy change for reversible processes

The second part of the Second Law states that the entropy change of a system undergoing a reversible process is given by:

$dS={\frac {\delta Q}{T}}$

where the temperature is defined as:

${\frac {1}{k_{\mathrm {B} }T}}\equiv \beta \equiv {\frac {d\ln \left[\Omega \left(E\right)\right]}{dE}}$

See here for the justification for this definition. Suppose that the system has some external parameter, x, that can be changed. In general, the energy eigenstates of the system will depend on x. According to the adiabatic theorem of quantum mechanics, in the limit of an infinitely slow change of the system's Hamiltonian, the system will stay in the same energy eigenstate and thus change its energy according to the change in energy of the energy eigenstate it is in.

The generalized force, X, corresponding to the external variable x is defined such that $Xdx$ is the work performed by the system if x is increased by an amount dx. E.g., if x is the volume, then X is the pressure. The generalized force for a system known to be in energy eigenstate $E_{r}$ is given by:

$X=-{\frac {dE_{r}}{dx}}$

Since the system can be in any energy eigenstate within an interval of $\delta E$, we define the generalized force for the system as the expectation value of the above expression:

$X=-\left\langle {\frac {dE_{r}}{dx}}\right\rangle \,$

To evaluate the average, we partition the $\Omega \left(E\right)$ energy eigenstates by counting how many of them have a value for ${\frac {dE_{r}}{dx}}$ within a range between $Y$ and $Y+\delta Y$. Calling this number $\Omega _{Y}\left(E\right)$, we have:

$\Omega \left(E\right)=\sum _{Y}\Omega _{Y}\left(E\right)\,$

The average defining the generalized force can now be written:

$X=-{\frac {1}{\Omega \left(E\right)}}\sum _{Y}Y\Omega _{Y}\left(E\right)\,$

We can relate this to the derivative of the entropy w.r.t. x at constant energy E as follows. Suppose we change x to x + dx. Then $\Omega \left(E\right)$ will change because the energy eigenstates depend on x, causing energy eigenstates to move into or out of the range between $E$ and $E+\delta E$. Let's focus again on the energy eigenstates for which ${\frac {dE_{r}}{dx}}$ lies within the range between $Y$ and $Y+\delta Y$. Since these energy eigenstates increase in energy by Y dx, all such energy eigenstates that are in the interval ranging from E – Y dx to E move from below E to above E. There are

$N_{Y}\left(E\right)={\frac {\Omega _{Y}\left(E\right)}{\delta E}}Ydx\,$

such energy eigenstates. If $Ydx\leq \delta E$, all these energy eigenstates will move into the range between $E$ and $E+\delta E$ and contribute to an increase in $\Omega$. The number of energy eigenstates that move from below $E+\delta E$ to above $E+\delta E$ is, of course, given by $N_{Y}\left(E+\delta E\right)$. The difference

$N_{Y}\left(E\right)-N_{Y}\left(E+\delta E\right)\,$

is thus the net contribution to the increase in $\Omega$. Note that if Y dx is larger than $\delta E$ there will be the energy eigenstates that move from below E to above $E+\delta E$. They are counted in both $N_{Y}\left(E\right)$ and $N_{Y}\left(E+\delta E\right)$, therefore the above expression is also valid in that case.

Expressing the above expression as a derivative w.r.t. E and summing over Y yields the expression:

$\left({\frac {\partial \Omega }{\partial x}}\right)_{E}=-\sum _{Y}Y\left({\frac {\partial \Omega _{Y}}{\partial E}}\right)_{x}=\left({\frac {\partial \left(\Omega X\right)}{\partial E}}\right)_{x}\,$

The logarithmic derivative of $\Omega$ w.r.t. x is thus given by:

$\left({\frac {\partial \ln \left(\Omega \right)}{\partial x}}\right)_{E}=\beta X+\left({\frac {\partial X}{\partial E}}\right)_{x}\,$

The first term is intensive, i.e. it does not scale with system size. In contrast, the last term scales as the inverse system size and will thus vanishes in the thermodynamic limit. We have thus found that:

$\left({\frac {\partial S}{\partial x}}\right)_{E}={\frac {X}{T}}\,$

Combining this with

$\left({\frac {\partial S}{\partial E}}\right)_{x}={\frac {1}{T}}\,$

Gives:

$dS=\left({\frac {\partial S}{\partial E}}\right)_{x}dE+\left({\frac {\partial S}{\partial x}}\right)_{E}dx={\frac {dE}{T}}+{\frac {X}{T}}dx={\frac {\delta Q}{T}}\,$

Derivation for systems described by the canonical ensemble

If a system is in thermal contact with a heat bath at some temperature T then, in equilibrium, the probability distribution over the energy eigenvalues are given by the canonical ensemble:

$P_{j}={\frac {\exp \left(-{\frac {E_{j}}{k_{\mathrm {B} }T}}\right)}{Z}}$

Here Z is a factor that normalizes the sum of all the probabilities to 1, this function is known as the partition function. We now consider an infinitesimal reversible change in the temperature and in the external parameters on which the energy levels depend. It follows from the general formula for the entropy:

$S=-k_{\mathrm {B} }\sum _{j}P_{j}\ln \left(P_{j}\right)$

that

$dS=-k_{\mathrm {B} }\sum _{j}\ln \left(P_{j}\right)dP_{j}$

Inserting the formula for $P_{j}$ for the canonical ensemble in here gives:

$dS={\frac {1}{T}}\sum _{j}E_{j}dP_{j}={\frac {1}{T}}\sum _{j}d\left(E_{j}P_{j}\right)-{\frac {1}{T}}\sum _{j}P_{j}dE_{j}={\frac {dE+\delta W}{T}}={\frac {\delta Q}{T}}$

General derivation from unitarity of quantum mechanics

The time development operator in quantum theory is unitary, because the Hamiltonian is hermitian. Consequently, the transition probability matrix is doubly stochastic, which implies the Second Law of Thermodynamics. This derivation is quite general, based on the Shannon entropy, and does not require any assumptions beyond unitarity, which is universally accepted. It is a consequence of the irreversibility or singular nature of the general transition matrix.

Non-equilibrium states

It is only by convention, for the purposes of thermodynamic analysis, that any arbitrary occasion of space-time is said to be in thermodynamic equilibrium. In general, an occasion of space-time found in nature is not in thermodynamic equilibrium, read in the most stringent terms. In looser terms, nothing in the entire universe is or has ever been truly in exact thermodynamic equilibrium. If it is assumed, for the purposes of physical analysis, that one is dealing with a system in thermodynamic equilibrium, then statistically it is possible for that system to achieve moments of non-equilibrium. In some statistically unlikely events, hot particles "steal" the energy of cold particles, enough that the cold side gets colder and the hot side gets hotter, for a very brief time.

The physics involved in such events is beyond the scope of classical equilibrium thermodynamics, and is the topic of the fluctuation theorem (not to be confused with the fluctuation-dissipation theorem). This was first proved by Bochov and Kuzovlev, and later by Evans and Searles. It gives a numerical estimate of the probability that a system away from equilibrium will have a certain change in entropy over a certain amount of time. The theorem is proved with the exact time reversible dynamical equations of motion but assumes the Axiom of Causality, which is equivalent to assuming uncorrelated initial conditions (namely, uncorrelated past). Such events have been observed at a small enough scale where the likelihood of such a thing happening is significant. Quantitative predictions of this theorem have been confirmed in laboratory experiments by use of optical tweezers apparatus.

Arrow of time

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The second law has been proposed to supply an explanation of the difference between moving forward and backwards in time, such as why the cause precedes the effect (the causal arrow of time).

Controversies

Maxwell's demon

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James Clerk Maxwell

James Clerk Maxwell imagined one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics.

One of the most famous responses to this question was suggested in 1929 by Leó Szilárd and later by Léon Brillouin. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy.

Loschmidt's paradox

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. This puts the time reversal symmetry of nearly all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behavior of macroscopic systems. Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict; hence the paradox.

Due to this paradox, derivations of the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past, or - equivalently - that the entropy in the past was lower than in the future. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately derived from the initial conditions of the Big Bang.

Gibbs paradox

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. In statistical mechanics, a simple derivation of the entropy of an ideal gas of distinguishable particles based on the canonical ensemble yields an expression for the entropy which is not extensive (is not proportional to the amount of gas in question). This leads to an apparent paradox known as the Gibbs paradox, allowing, for instance, the entropy of closed systems to decrease, violating the second law of thermodynamics.

The paradox is averted by recognizing that the identity of the particles does not influence the entropy. In the conventional explanation, this is associated with an indistinguishability of the particles associated with quantum mechanics. However, a growing number of papers now take the perspective that it is merely the definition of entropy that is changed to ignore particle permutation (and thereby avert the paradox). The resulting equation for the entropy (of a classical ideal gas) is extensive, and is known as the Sackur-Tetrode equation.

Poincaré recurrence theorem

The Poincaré recurrence theorem states that certain systems will, after a sufficiently long time, return to a state very close to the initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence, which is of the order of $\sim \exp \left(S/k\right)$. The result applies to physical systems in which energy is conserved. The Recurrence theorem apparently contradicts the Second law of thermodynamics, which says that large dynamical systems evolve irreversibly towards the state with higher entropy, so that if one starts with a low-entropy state, the system will never return to it. There are many possible ways to resolve this paradox, but none of them is universally accepted.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. The most reasonable argument is that for typical thermodynamical systems the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence.

Future of the universe

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. It has been suggested in the past that since the entropy in the universe is continuously rising, the amount of free energy diminishes and the universe will arrive at a heat death, in which no work can be done and life cannot exist. An expanding universe, however, is not in a thermodynamical equilibrium, and simple considerations leading to the heat death scenario are not valid.

Taking the current view of the universe into account, it has been proposed that the universe will probably exhibit a future in which all known energy sources (such as stars) will decay. Nevertheless, it may be the case that work in smaller and smaller energy scales will still be possible, so that "interesting things can continue to happen at ... increasingly low levels of energy".

Quotations

Property growth may be attributed as the enhancement of a given space by an individual or a marketing consultant or by a corporation as a whole. Any particular person or organization involved in the above activity will possible be known as a Property Developer. Singapore is admittedly well-known in Asia for its booming property.

As a Singapore citizen and in case you are eligible for the backed loans you may benefit from the backed mortgage rates of the HDB. The HDB can grant a sponsored mortgage to first time house patrons and also to second time house consumers who upgrade to another HDB flats. Beginning of January 2008 ,the Singapore Inter financial institution offered rate (Sibor) has fallen again and is at its lowest since three years. Analysts consider it's going to sink additional throughout 2008. The Sibor is the speed at which bank lend to one another and influences what you pay for a mortgage. Statistics exhibits nonetheless, that local and foreign banks in Singapore don't go on the savings without delay but fairly in a time-frame from about two months. Read Extra Do rising Singapore bankruptcies signal hassle ahead?

One in every of Asia's premier property companies, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and investment-grade commercial properties in addition to excessive requirements of corporate governance and transparency. Keppel Land is likely one of the largest listed property companies by whole belongings on the Singapore Change. The Group's complete assets amounted to about $13.eight billion as at 31 March 2014. It is usually a element of several stock indices together with the FTSE ST Actual Estate Index, FTSE ST China High Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Property Index and EPRA/NAREIT Index. WOODSVALE PERSONAL CONDOMINIUM CONDO WOODSVALE SHUT, SINGAPORE (DISTRICT thirteen) Industrial

The rise within the nominal value index pales as compared with the 38.2% value hike (34% in actual terms) throughout the 12 months to Q2 2010, a period which noticed the fastest value-rises of the recent increase. Measures were introduced in October 2012 to limit mortgage tenure to 35 years, and to lower to 60% the LTV ratio for loans longer than 30 years, or mortgage durations extending past age sixty five. Client Worth Index for Households in Completely different Revenue Teams Domestic Provide Price Index Home Wholesale Commerce Index Expenditure on Gross Domestic Product at 2005 Market Costs Expenditure on Gross Domestic Product at Current Market Prices Food & Beverage Services Index Authorities Improvement Expenditure Gross Home Product at 2005 Market Costs Gross Home Product at Current Market Prices

Thinking of buying property in Singapore and wish to know extra about particular property launches in Singapore, or to attend their VIP Previews ? If you've ever had the experience of paying for an uncompleted property elsewhere only to see the developer vanish halfway by construction of the venture, you'd be glad to know this isn't one thing that's more likely to occur should you're shopping for property in Singapore. That's as a result of new Singapore property gross sales are very high regulated. This page covers some temporary data on the procedures to buy or purchase property in Singapore. Tips for foreigners or buyers buying condominium, home or other properties in Singapore. the title of the big property developers in singapore; Landed Property Builders step by step raising property prices HDB HUB

Only Singapore citizens and accepted persons should buy Landed 'residential property'as outlined in the Residential Properties Act. Foreigners are eligible to purchaseunits in condominiums or flats which aren't landed dwelling homes. Foreignerswho wish to buy landed property in Singapore should first search the approval ofthe Controller of Residential Property. Your Lawyer's Function in a Property Purchase Pending completion of your buy, your lawyer will lodge a caveat towards the title to the property - this serves to notify the general public (and any third social gathering fascinated in the property) that you've a sound curiosity or declare to the title of the property arising from the contract for the sale and buy. Property was all the time on his thoughts Property

Non-public residential properties investment shall be thought of for software for Everlasting Resident software. A foreigner will be considered for PR status if he invests at the least S$2 million in business set-ups, other funding autos such as venture capital funds, foundations or trusts, and/or private residential properties. Up to 50% of the funding may be in personal residential properties, topic to foreign ownership restrictions underneath the Residential Property Act (RPA). That is to attract and anchor foreign expertise in Singapore.

NASSIM, THE PERSONAL CONDOMINIUM CONDOMINIUM NASSIM HILL, SINGAPORE (DISTRICT 10) NATHAN RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE NATHAN STREET, SINGAPORE (DISTRICT 10) NATHAN SUITES PERSONAL CONDOMINIUM RESIDENCE NATHAN STREET, SINGAPORE (DISTRICT 10) NAUTICAL, THE PRIVATE CONDOMINIUM CONDO JALAN SENDUDOK, SINGAPORE (DISTRICT 27) NINE DEGRESS (LAUNCHING QUICKLY!) PRIVATE CONDOMINIUM APARTMENT TANJONG KATONG ROAD, SINGAPORE (DISTRICT 15) NOUVEL 18 NON-PUBLIC CONDOMINIUM RESIDENCE ANDERSON STREET, SINGAPORE (DISTRICT 09) ONE DUSUN RESIDENCES NON-PUBLIC CONDOMINIUM CONDOMINIUM JALAN DUSUN, BALESTIER ROAD, SINGAPORE (DISTRICT 12) ONE DUSUN RESIDENCES INDUSTRIAL RETAIL STORE HOUSE JALAN DUSUN, BALESTIER ROAD, SINGAPORE (DISTRICT 12) Wing Tai Holdings Ltd Singapore 31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape. 31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape. 31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape. 31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape. 31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape.

See also

• Clausius–Duhem inequality
• Entropy: A New World View
• History of thermodynamics
• Jarzynski equality
• Laws of thermodynamics
• Maximum entropy thermodynamics
• Reflections on the Motive Power of Fire
• Thermal diode
• Relativistic heat conduction

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro. Template:Refend

Bibliography of citations

• Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, ISBN 0-521-25445-0.
• Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics, New York, ISBN 0-88318-797-3.
• Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, Cambridge UK.
• Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8.
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang. A translation may be found here. Also a mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA.
• Carnot, S. (1824/1986). Reflections on the motive power of fire, Manchester University Press, Manchester UK, ISBN 0719017416. Also here.
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Translated into English: One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• Eu, B.C. (2002). Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics, Kluwer Academic Publishers, Dordrecht, ISBN 1–4020–0788–4.
• Grandy, W.T., Jr (2008). Entropy and the Time Evolution of Macroscopic Systems. Oxford University Press. ISBN 978-0-19-954617-6.
• Kondepudi, D., Prigogine, I. (1998). Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wiley & Sons, Chichester, ISBN 0–471–97393–9.
• Lebon, G., Jou, D., Casas-Vázquez, J. (2008). Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers, Springer-Verlag, Berlin, e-ISBN 978-3-540-74252-4.
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• Münster, A. (1970), Classical Thermodynamics, translated by E.S. Halberstadt, Wiley–Interscience, London, ISBN 0-471-62430-6.
• Planck, M. (1926). Über die Begründing des zweiten Hauptsatzes der Thermodynamik, S.B. Preuß. Akad. Wiss. phys. math. Kl.: 453–463.
• Quinn, T.J. (1983). Temperature, Academic Press, London, ISBN 0-12-569680-9.
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Also published in One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• Truesdell, C. (1980). The Tragicomical History of Thermodynamics 1822-1854, Springer, New York, ISBN 0–387–90403–4.
• Zemansky, M.W. (1968). Heat and Thermodynamics. An Intermediate Textbook, fifth edition, McGraw-Hill Book Company, New York.

Further reading

• Goldstein, Martin, and Inge F., 1993. The Refrigerator and the Universe. Harvard Univ. Press. Chpts. 4–9 contain an introduction to the Second Law, one a bit less technical than this entry. ISBN 978-0-674-75324-2
• Leff, Harvey S., and Rex, Andrew F. (eds.) 2003. Maxwell's Demon 2 : Entropy, classical and quantum information, computing. Bristol UK; Philadelphia PA: Institute of Physics. ISBN 978-0-585-49237-7
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534(technical).
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 (full text of 1897 ed.)) (html)
• Stephen Jay Kline (1999). The Low-Down on Entropy and Interpretive Thermodynamics, La Cañada, CA: DCW Industries. ISBN 1928729010.
• Kostic, M., Revisiting The Second Law of Energy Degradation and Entropy Generation: From Sadi Carnot's Ingenious Reasoning to Holistic Generalization.
• AIP Conf. Proc. 1411, pp. 327–350; doi: http://dx.doi.org/10.1063/1.3665247. American Institute of Physics, 2011. ISBN 978-0-7354-0985-9. Abstract at: [1]. Full article (24 pages [2]), also at [3].

External links

• Stanford Encyclopedia of Philosophy: "Philosophy of Statistical Mechanics" – by Lawrence Sklar.
• Second law of thermodynamics in the MIT Course Unified Thermodynamics and Propulsion from Prof. Z. S. Spakovszky
• E.T. Jaynes, 1988, "The evolution of Carnot's principle," in G. J. Erickson and C. R. Smith (eds.)Maximum-Entropy and Bayesian Methods in Science and Engineering, Vol 1, p. 267.
• Caratheodory, C., "Examination of the foundations of thermodynamics," trans. by D. H. Delphenich