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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.[1]
Mathematical formulation
In the canonical ensemble, the entropic force associated to a macrostate partition is given by: [2] [3][4]
where is the temperature, is the entropy associated to the macrostate and is the present macrostate.
Examples
Brownian Motion
Entropic approach to Brownian movement is initially proposed by R. M. Neumann,[5] .[6] 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 electrostatic system of molten salt, surface tension and rubber elasticity.
Polymers
A standard example of an entropic force is the elasticity of a freely-jointed polymer molecule described by a Gaussian distribution.[6] 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
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Another example of an entropic force is the 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 dissolved substance. Each water molecule is capable of
- donating two hydrogen bonds through the two protons
- accepting two more hydrogen bonds through the two sp3-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 sp3 orbitals.[7] 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 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.[8] This was later proven to be correct[9][10] and allowed for the development of a roadmap for the assembly of polyhedral particles into atomic isostructures.[11]
Speculative examples
In recent years (especially since 2009) 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. some forces that are generally regarded as conventional forces have been argued to be actually entropic in nature. These theories remain speculative and are the subject of ongoing work.
Gravity
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 is generally believed that gravity is a microscopic forcePotter 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. (or arguably a pseudo-force in general relativity where it becomes a pseudo-scalar at the Planck length scale). However, in 2009, Erik Verlinde[12] argued that gravity can be explained as an entropic force.[13]
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."Template:Clarify 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.[3]
Other forces
Other fundamental forces have been argued recently to be entropic in origin, including Coulomb's law,[14][15][16] the electroweak and strong forces,[17] and dark matter and dark energy.[18]
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[19] in the context of Occam's razor principle.
See also
References
- ↑ A history of thermodynamics: the doctrine of energy and entropy by Ingo Müller, p115
- ↑ Entropic approach to Brownian movement; See Richard M. Neumann, Am. J. Phys. 48, 354 (1980) http://dx.doi.org/10.1119/1.12095
- ↑ 3.0 3.1 Causal entropic forces, Alex Wissner-Gross, Physical Review Letters 110, 168702 (2013)
- ↑ On the origin of gravity and the laws of Newton, Erik Verlinde
- ↑ Entropic approach to Brownian movement; See Richard M. Neumann, Am. J. Phys. 48, 354 (1980) http://dx.doi.org/10.1119/1.12095
- ↑ 6.0 6.1 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
- ↑ Encyclopedia of Life Science Article on Hydrophobic Effect; See Figure 4: http://xibalba.lcg.unam.mx/~rgalindo/bioquimica/BQPosgrado2011/I%20FQ%20repaso/HydrophobicEffect.pdf
- ↑ Template:Cite web
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- ↑ Template:Cite arXiv
- ↑ 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
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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 - ↑ http://arxiv.org//abs/1001.4965, Coulomb Force as an Entropic Force, T. Wang
- ↑ http://arxiv.org//abs/0809.4631, Simple field theoretical approach of Coulomb systems. Entropic effects, D. di Caprio, J.P. Badiali, M. Holovko
- ↑ http://arxiv.org//abs/1009.5561, Entropic Corrections to Coulomb's Law, A. Sheykhi, S. H. Hendi
- ↑ http://arxiv.org//abs/1008.4147, Emergent Gauge Fields, Peter G.O. Freund
- ↑ 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
- ↑ 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).