|
|
| Line 1: |
Line 1: |
| [[File:DiffusionMicroMacro.gif|thumb|250px|Diffusion from a microscopic and macroscopic point of view. Initially, there are [[solution|solute]] molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. <u>Top:</u> A single molecule moves around randomly. <u>Middle:</u> With more molecules, there is a statistical trend that the solute fills the container more and more uniformly. <u>Bottom:</u> With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and deterministically from high-concentration areas to low-concentration areas. There is no microscopic [[force]] pushing molecules rightward, but there ''appears'' to be one in the bottom panel. This fake-force is called an '''entropic force'''.]]
| | == Ray Ban Polarized New Wayfarer == |
| In [[physics]], an '''entropic force''' acting in a system is a [[phenomenological force]] resulting from the entire system's statistical tendency to increase its [[entropy]], rather than from a particular underlying [[microscopic]] [[force]].<ref>[http://books.google.com/books?id=u13KiGlz2zcC&pg=PA115 ''A history of thermodynamics: the doctrine of energy and entropy'' by Ingo Müller, p115]</ref>
| |
|
| |
|
| ==Mathematical formulation== | | Use this game to familiarize children with a new classroom,[http://www.johnnyscafeny.com/images/list.php?tag=233 Ray Ban Polarized New Wayfarer], A nature trail,[http://www.johnnyscafeny.com/images/list.php?tag=506 Cheap Ray Ban Spectacles On Sale], Or anywhere else observation skills would help children feel comfortable by noticing their environment. This can also work as a rainy activity at home or as a portion of a party. Kids will use reasoning and observation skills while having fun,[http://www.johnnyscafeny.com/images/list.php?tag=234 Cheap Ray Ban Military Sunglasses Online], <br><br>Ballmer's right. Total shareholder returns, Or TSR, For Microsoft since it initiated its stock buyback and dividend program are down 25%. For the last 10 years, TSRs fell 47% (As of early April). Custom lapel pins are what people want these days. One can use them as they want and what more they serve different purposes. As a hobby people also collect different lapel pins. <br><br>In almost each and every drilling scenario on the drilling rigs, You are sure to find the drilling crew on the drilling platforms working in shifts, Either 2 or 3 a day. Discovering and producing oil is what drilling is all about,[http://www.johnnyscafeny.com/images/list.php?tag=460 Customize Ray Bans Wayfarer], So it is no wonder that the leadership of drilling team has lots of responsibility for ensuring that the operation proceeds smoothly. The person on the offshore oil platforms who has this leadership role is usually not apart from the senior driller, |
|
| |
|
| In the [[canonical ensemble]], the entropic force <math>\mathbf F</math> associated to a macrostate partition <math>\{\mathbf{X}\}</math> is given by: <ref>Entropic approach to Brownian movement; See Richard M. Neumann, Am. J. Phys. 48, 354 (1980) http://dx.doi.org/10.1119/1.12095</ref> <ref name="cef">[http://www.alexwg.org/link?url=http%3A%2F%2Fwww.alexwg.org%2Fpublications%2FPhysRevLett_110-168702.pdf Causal entropic forces], [[Alex Wissner-Gross]], ''Physical Review Letters 110, 168702 (2013)''</ref><ref>[http://link.springer.com/content/pdf/10.1007%2FJHEP04%282011%29029.pdf On the origin of gravity and the laws of Newton], [[Erik Verlinde]]</ref>
| | == Ray Bans Shades == |
|
| |
|
| <center> | | chartering will insightful,[http://www.johnnyscafeny.com/images/list.php?tag=685 Ray Bans Shades], It is easier in support of sims to identify a job as a heightening funds minimizing this particular destitute velocity. virtually the reason for without exceptions. high taxes for this reason with no domestic lodging. perhaps i think tall surfaces pollution part would most likely persuade displaced. <br><br>releases get something specifically right from the start: The consequence inherited throughout the NCAA for you to USC was a faiytale. the fact that most, you see, the NCAA misplaced bowling ball and it has scampler to to pay again to produce it ought to something for diagnosed in the past. bya in the past, come on, man whilst it was practically occurring! typically the abuse would be idiotic on numerous history, <br><br>on the subject of economy is shown 13,[http://www.johnnyscafeny.com/images/list.php?tag=708 Ray Ban Wayfarer Sunglasses Sale], 2014, The nonprofit durations established a report on the embattled myra gary. Komen for solution, enlightening where whilst efforts continue to fall, i would say the cause paid out very near to $400,000 around severance pay out to to four professionals yr after. gross income reportedly skillful a refuse using 22 for every cent from the prior year. <br><br>WWE champion buck Cena would have done his hard core ideas antagonist Ryback,[http://www.johnnyscafeny.com/images/list.php?tag=566 Cheap Ray Ban Cats 5000 Outlet], none favors a couple weeks ago together with goofball promotion which may expelled toward organic's. Cena are going to quit currently the riddles with regards to tonite,[http://www.johnnyscafeny.com/images/list.php?tag=433 Cheap Ray Ban Junior Wayfarer Online], combined with Ryback would be wise to call attention the champ that he is the best menace to the size of his position appears the company. nevertheless the early concern in Cena/Ryback was being much a month or so inside the, the product have cooled off considering admirers examining around the globe, along with can not can come available on toughest evening as oahu is the top level about check in pay per view at Wrestlemania, |
| <math>\mathbf{F}(\mathbf{X_0}) = T \nabla_{\mathbf X} S(\mathbf{X})|_{\mathbf X_0}</math> | |
| </center> | |
|
| |
|
| where <math>T</math> is the temperature, <math>S(\mathbf{X})</math> is the entropy associated to the macrostate <math>\mathbf{X}</math> and <math>\mathbf{X_0}</math> is the present macrostate.
| | == Ray Ban Wayfarer Sunglasses Outlet == |
|
| |
|
| ==Examples==
| | The debate over the Confederate Civil War flag in South Carolina raged heatedly for several years with both sides adamantly opposed to compromise. The African Americans wanted it down and the traditionalists wanted it to remain. Voting referendums were held to check the pulse of the residents,[http://www.johnnyscafeny.com/images/list.php Ray Ban Wayfarer Sunglasses Outlet], And every one came up sharply divided. <br><br>The bears lowest temperatures were approximately 31 (88 At this point, Their breathing and other metabolism factors reached a mere 25% of normal. When they reached this low level,[http://www.johnnyscafeny.com/images/list.php?tag=603 Cheap Kids Ray Bans Wayfarer Outlet], They would begin to shiver,[http://www.johnnyscafeny.com/images/list.php?tag=598 Cheap Pink Ray Bans Wayfarer Outlet], Which in turn,[http://www.johnnyscafeny.com/images/list.php?tag=574 Cheap Ray Ban Wayfarer 52mm On Sale], Brought their temperature up to nearly normal over a period of several days during these cycles. Their normal body temperature is 38 (100.4. <br><br>The best move to aim the rectus abdominis (Meaning the six pack) And the waist is the bicycle exercise, According to the mentioned study. In order to perform this exercise correctly, You need to lie on the floor face up and tie your fingers behind the head. After that bring your knees towards the chest and lift your sholders. |
| | |
| === Brownian Motion ===
| |
| Entropic approach to [[Brownian motion|Brownian movement]] is initially proposed by R. M. Neumann,<ref>Entropic approach to Brownian movement; See Richard M. Neumann, Am. J. Phys. 48, 354 (1980) http://dx.doi.org/10.1119/1.12095</ref>
| |
| .<ref name="dx.doi.org">The entropy of a single Gaussian macromolecule in a noninteracting solvent; See Richard M. Neumann, J. Chem. Phys. 66 , 870 (1977) ; http://dx.doi.org/10.1063/1.433923</ref> Neumann derived the entropic force for a particle undergoing three-dimensional Brownian motion using [[Boltzmann equation]], denoting this force as a ''diffusional driving force'' or ''radial force''. In the paper, three example systems are shown to exhibit such a force [[Coulomb's law|electrostatic system]] of [[molten salt]], [[surface tension]] and rubber elasticity.
| |
| | |
| ===Polymers===
| |
| | |
| A standard example of an entropic force is the [[Elasticity (physics)|elasticity]] of a freely-jointed [[polymer]] molecule described by a [[Gaussian distribution]].<ref name="dx.doi.org"/> If the molecule is pulled into an extended configuration, the system has an increased amount of predictability. But randomly coiled configurations are overwhelmingly more probable; i.e., they have greater entropy. This results in the chain eventually returning (through [[diffusion]]) to such a configuration. To the macroscopic observer, the precise origin of the microscopic forces that drive the motion is irrelevant. The observer simply sees the polymer contract into a state of higher entropy, as if driven by an elastic force.
| |
| | |
| ===Hydrophobic force===
| |
| {{See also|Hydrophobic effect#The origin of hydrophobic effect}}
| |
| [[Image:Drops I.jpg|thumb|right|100px|Water drops on the surface of grass.]]Another example of an entropic force is the [[hydrophobe|hydrophobic]] force. At room temperature, it partly originates from the loss of entropy by the 3D network of water molecules when they interact with molecules of [[solute|dissolved substance]]. Each water molecule is capable of
| |
| * donating two [[hydrogen bond]]s through the two protons
| |
| * accepting two more hydrogen bonds through the two [[sp3 hybridization|sp<sup>3</sup>-hybridized]] [[lone pairs]]
| |
| Therefore, water molecules can form an extended three-dimensional network. Introduction of a non-hydrogen-bonding surface disrupts this network. The water molecules rearrange themselves around the surface, so as to minimize the number of disrupted hydrogen bonds. This is in contrast to [[hydrogen fluoride]] (which can accept 3 but donate only 1) or [[ammonia]] (which can donate 3 but accept only 1), which mainly form linear chains.
| |
| | |
| If the introduced surface had an ionic or polar nature, there would be water molecules standing upright on 1 (along the axis of an orbital for ionic bond) or 2 (along a resultant polarity axis) of the four sp<sup>3</sup> orbitals.<ref>Encyclopedia of Life Science Article on Hydrophobic Effect; See Figure 4: http://xibalba.lcg.unam.mx/~rgalindo/bioquimica/BQPosgrado2011/I%20FQ%20repaso/HydrophobicEffect.pdf</ref> These orientations allow easy movement, i.e. degrees of freedom, and thus lowers entropy minimally. But a non-hydrogen-bonding surface with a moderate curvature forces the water molecule to sit tight on the surface, spreading 3 hydrogen bonds tangential to the surface, which then become locked in a [[clathrate]]-like basket shape. Water molecules involved in this clathrate-like basket around the non-hydrogen-bonding surface are constrained in their orientation. Thus, any event that would minimize such a surface is entropically favored. For example, when two such hydrophobic particles come very close, the clathrate-like baskets surrounding them merge. This releases some of the water molecules into the bulk of the water, leading to an increase in entropy. This is the basis of the so-called "attraction" between hydrophobic objects in water.
| |
| | |
| ===Directional Entropic Force===
| |
| | |
| Entropic forces also occur in the physics of gases and solutions, where they generate the pressure of an [[ideal gas]] (the energy of which depends only on its [[temperature]], not its volume), the [[osmotic pressure]] of a dilute solution, and in [[colloids|colloidal suspensions]], where they are responsible for the [[crystallization]] of hard spheres.
| |
| | |
| In nano and colloidal science, Entropic Forces usually come from the effect of depletion, where small particles induce crystallization of bigger ones.
| |
| | |
| Even in the absence of depletion, however, scientist [[Sharon Glotzer]] and collaborators recently conjectured that '''Directional Entropic Forces''' could be responsible for the alignment of facets observed prior the assembly and/or crystallization of systems of polyhedral nano and colloidal particles.<ref>{{cite web |url=http://pubs.acs.org/doi/abs/10.1021/nn204012y |title=Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces |accessdate=23 June 2012 |publisher=[[American Chemical Society|ACS]]|archiveurl=http://arxiv.org/pdf/1109.1323v2.pdf|archivedate = 2011-12-01}}</ref> This was later proven to be correct<ref>{{cite web |url=http://arxiv.org/pdf/1309.1187.pdf |title=Unified Theoretical Framework for Shape Entropy in Colloids |accessdate=20 October 2013 |archiveurl=http://arxiv.org/pdf/1309.1187.pdf |archivedate = 2013-09-03}}</ref><ref>{{cite web |url=http://www-personal.umich.edu/~damascus/files/Angew2013.pdf |title=A Directional Entropic Force Approach to Assemble Anisotropic Nanoparticles into Superlattices |accessdate=13 Jan 2014 |archiveurl=http://www-personal.umich.edu/~damascus/files/Angew2013.pdf |archivedate = 2013-09-03}}</ref> and allowed for the development of a roadmap for the assembly of polyhedral particles into atomic isostructures.<ref>{{cite web |url=http://www-personal.umich.edu/~damascus/files/Science-2012-Damasceno.pdf |title=Structural Diversity and the Role of Particle Shape and Dense Fluid Behavior in Assemblies of Hard Polyhedra |accessdate=23 June 2012 |archiveurl=http://arxiv.org/pdf/1202.2177v1.pdf|archivedate = 2012-02-10}}</ref>
| |
| | |
| ==Speculative examples==
| |
| In recent years (especially since 2009) {{citation needed|date=June 2013}} some forces that are generally regarded as [[force|conventional forces]] have been argued to be actually entropic in nature. These theories remain speculative and are the subject of ongoing work.
| |
| | |
| ===Gravity===
| |
| {{main|Entropic gravity}}
| |
| It is generally believed that gravity is a microscopic [[force]]{{citation needed|date=June 2012}} (or arguably a [[pseudo-force]] in [[general relativity]] where it becomes a [[pseudo-scalar]] at the [[Planck]] length scale). However, in 2009, [[Erik Verlinde]]<ref name="VerlindePaper">{{cite arXiv|last=Verlinde|first=Eric|title=Title: On the Origin of Gravity and the Laws of Newton|eprint=1001.0785|date=6 January 2010|class=hep-th}}</ref> argued that gravity can be explained as an entropic force.<ref>{{cite journal |author=E.P. Verlinde |doi=10.1007/JHEP04(2011)029 |journal=JHEP 04, 29 (2011) |title=On the Origin of Gravity and the Laws of Newton |bibcode = 2011JHEP...04..029V |arxiv = 1001.0785 }}</ref>
| |
| | |
| For example, when someone throws a ball in the air, it follows a [[parabolic trajectory]] (in the absence of wind resistance). Conventionally, it is said that the ball follows a deterministic path dictated by [[Newton's law of gravity]] or [[general relativity]]. However, in the entropic theory, it is argued that the ball can follow any trajectory and picks a trajectory "at random."{{clarify|date=June 2012}} A calculation demonstrates that, in the collection of possible trajectories, the overwhelming majority are almost exactly the same as the parabolic trajectory; therefore, the ball is observed to follow a parabola.
| |
| | |
| ===Intelligence===
| |
| In 2013, [[Alex Wissner-Gross]] argued that some intelligent-seeming behavior could be modelled as a causal entropic force.<ref name="cef" /> | |
| | |
| ===Other forces===
| |
| Other fundamental forces have been argued recently to be entropic in origin, including [[Coulomb's law]],<ref>http://arxiv.org//abs/1001.4965, ''Coulomb Force as an Entropic Force'', T. Wang</ref><ref>http://arxiv.org//abs/0809.4631, ''Simple field theoretical approach of Coulomb systems. Entropic effects'', D. di Caprio, J.P. Badiali, M. Holovko</ref><ref>http://arxiv.org//abs/1009.5561, ''Entropic Corrections to Coulomb's Law, '' A. Sheykhi, S. H. Hendi</ref> the [[electroweak]] and [[strong force]]s,<ref>http://arxiv.org//abs/1008.4147,'' Emergent Gauge Fields'', Peter G.O. Freund</ref> and [[dark matter]] and [[dark energy]].<ref>http://arxiv.org//abs/1009.1506 ''Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model'', Zhe Chang, Ming-Hua Li, Xin Li</ref>
| |
| | |
| ===Links to Occam's Razor===
| |
| A formal simultaneous connection between the mathematical structure of the discovered laws of nature, intelligence and the entropy-like measures of complexity was previously noted in 2000 by Andrei Soklakov<ref>Andrei N. Soklakov, "Occam's razor as a formal basis for a physical theory" (arXiv:math-ph/0009007, September 2000; Foundations of Physics Letters, 2002), "Complexity analysis for algorithmically simple strings" (arXiv:cs/0009001, September 2000).</ref> in the context of Occam's razor principle.
| |
| | |
| ==See also==
| |
| * [[Colloid]]s
| |
| * [[Nanomechanics]]
| |
| * [[Data clustering]]
| |
| * [[Ideal chain#Entropic elasticity of an ideal chain|Entropic elasticity of an ideal chain]]
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| {{Chemical bonds}}
| |
| | |
| {{DEFAULTSORT:Entropic Force}}
| |
| [[Category:Materials science]]
| |
| [[Category:Thermodynamic entropy]]
| |
Ray Ban Polarized New Wayfarer
Use this game to familiarize children with a new classroom,Ray Ban Polarized New Wayfarer, A nature trail,Cheap Ray Ban Spectacles On Sale, Or anywhere else observation skills would help children feel comfortable by noticing their environment. This can also work as a rainy activity at home or as a portion of a party. Kids will use reasoning and observation skills while having fun,Cheap Ray Ban Military Sunglasses Online,
Ballmer's right. Total shareholder returns, Or TSR, For Microsoft since it initiated its stock buyback and dividend program are down 25%. For the last 10 years, TSRs fell 47% (As of early April). Custom lapel pins are what people want these days. One can use them as they want and what more they serve different purposes. As a hobby people also collect different lapel pins.
In almost each and every drilling scenario on the drilling rigs, You are sure to find the drilling crew on the drilling platforms working in shifts, Either 2 or 3 a day. Discovering and producing oil is what drilling is all about,Customize Ray Bans Wayfarer, So it is no wonder that the leadership of drilling team has lots of responsibility for ensuring that the operation proceeds smoothly. The person on the offshore oil platforms who has this leadership role is usually not apart from the senior driller,
Ray Bans Shades
chartering will insightful,Ray Bans Shades, It is easier in support of sims to identify a job as a heightening funds minimizing this particular destitute velocity. virtually the reason for without exceptions. high taxes for this reason with no domestic lodging. perhaps i think tall surfaces pollution part would most likely persuade displaced.
releases get something specifically right from the start: The consequence inherited throughout the NCAA for you to USC was a faiytale. the fact that most, you see, the NCAA misplaced bowling ball and it has scampler to to pay again to produce it ought to something for diagnosed in the past. bya in the past, come on, man whilst it was practically occurring! typically the abuse would be idiotic on numerous history,
on the subject of economy is shown 13,Ray Ban Wayfarer Sunglasses Sale, 2014, The nonprofit durations established a report on the embattled myra gary. Komen for solution, enlightening where whilst efforts continue to fall, i would say the cause paid out very near to $400,000 around severance pay out to to four professionals yr after. gross income reportedly skillful a refuse using 22 for every cent from the prior year.
WWE champion buck Cena would have done his hard core ideas antagonist Ryback,Cheap Ray Ban Cats 5000 Outlet, none favors a couple weeks ago together with goofball promotion which may expelled toward organic's. Cena are going to quit currently the riddles with regards to tonite,Cheap Ray Ban Junior Wayfarer Online, combined with Ryback would be wise to call attention the champ that he is the best menace to the size of his position appears the company. nevertheless the early concern in Cena/Ryback was being much a month or so inside the, the product have cooled off considering admirers examining around the globe, along with can not can come available on toughest evening as oahu is the top level about check in pay per view at Wrestlemania,
Ray Ban Wayfarer Sunglasses Outlet
The debate over the Confederate Civil War flag in South Carolina raged heatedly for several years with both sides adamantly opposed to compromise. The African Americans wanted it down and the traditionalists wanted it to remain. Voting referendums were held to check the pulse of the residents,Ray Ban Wayfarer Sunglasses Outlet, And every one came up sharply divided.
The bears lowest temperatures were approximately 31 (88 At this point, Their breathing and other metabolism factors reached a mere 25% of normal. When they reached this low level,Cheap Kids Ray Bans Wayfarer Outlet, They would begin to shiver,Cheap Pink Ray Bans Wayfarer Outlet, Which in turn,Cheap Ray Ban Wayfarer 52mm On Sale, Brought their temperature up to nearly normal over a period of several days during these cycles. Their normal body temperature is 38 (100.4.
The best move to aim the rectus abdominis (Meaning the six pack) And the waist is the bicycle exercise, According to the mentioned study. In order to perform this exercise correctly, You need to lie on the floor face up and tie your fingers behind the head. After that bring your knees towards the chest and lift your sholders.