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Entropic force 
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#1
Mar2411, 08:59 PM

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In the article for "ideal chain", http://en.wikipedia.org/wiki/Ideal_chain, wikipedia states
"If the two free ends of an ideal chain are attached to some kind of micromanipulation device, then the device experiences a force exerted by the polymer. The ideal chain's energy is constant, and thus its timeaverage, the internal energy, is also constant, which means that this force necessarily stems from a purely entropic effect." Could somebody explain what it means for the force on the polymer to be "purely entropic"? The force is clearly electromagnetic: molecules in its bath are jostling it around, and eventually it ends up in a higher entropy state. 


#2
Mar2511, 12:39 AM

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The change in energy with a change in coordinates (dE/dx) can be considered a force.
The jostlingaround proceeds by means of the electromagnetic force, but the change in energy isn't from a change in electromagnetic potential, but entropy. 


#3
Mar2511, 03:16 AM

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Some sources tend to describe entropic forces as something misterious. However, they are always due to real forces due to collisions of molecules of the heat bath with the macromolecules.
Think of a child holding the end of a rope that is tied to the wall and other children throwing balls at the rope. The child will have to do work against the force of the balls which on the average will tend to shorten the length of the rope, so somehow it is statistical but nevertheless it is due to the concrete collisions of the rope with the balls. On the other hand, any mechanical force excerted by a thermodynamic machine, e.g. a steam engine, can be thought of as being an entropic force. 


#4
Mar2511, 08:05 AM

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Entropic force
I've found it useful to visualize a chain in the bed of a pickup truck, or a necklace on a shaker table. Stretch it out into a straight line, and when you come back later you'll find that the ends have moved closer together. This is springlike behavior. But instead of electromagnetic attraction between atoms pulling the ends together (an enthalpic spring), it's thermal energy (represented in the visualization by mechanical agitation). Thus, an entropic spring.



#5
Mar2511, 08:16 AM

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Thanks for the responses. This is all consistent with what I believed, but it still seems crazy to call such a force "purely entropic", since the force is electromagnetic. I wouldn't object if they were just calling it an "entropic" force, although it of course can be a bit misleading to a newbie if they don't discuss the microscopic origin. But what is the word "purely" doing in there, if not purposely trying to mask the microscopic origin?
It might help if somebody knows of a thermodynamic example where force is not purely (but only partially) entropic. 


#6
Mar2511, 08:32 AM

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Besides, even without collisions from other atoms, a chain at any finite temperature would still tend to become disorganized because of the Second Law and the tendency for increasing entropy. The common element is entropy, not collisions, and definitely not electromagnetism. EDIT: Corrected "Heisenberg Uncertainty Principle" to "Pauli exclusion". 


#7
Mar2511, 11:32 AM

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#8
Mar2511, 12:32 PM

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Intermediate thermo books (e.g., Callen) derive how entropy maximization (Second Law) implies energy minimization, which is the reason why electric charges flow under voltage, fluids flow under pressure, surfaces are minimized, and objects move under force. You can't show me a force that doesn't arise from energy minimization, entropy maximization, or a combination of the two (such as when the Gibbs free energy is minimized to make reactions proceed at constant temperature and pressure). 


#9
Mar2511, 03:29 PM

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Mapes, your argument, although found in many books is flawed. You cannot assume at the same time that the entropy depends only on the length of the chain and on the other hand express the differential of U in terms of both S and L, or, what is the same, S in terms of U and L. If the chain is massless and isolated, with L being the only thermodynamical degree of freedom, it is not regular. If it is a chain where each element has a mass, then the entropy will not only depend on the length but also on the amount of kinetic energy, i.e, entropy will depend not only on the length of the chain but on phase space volume. Another interpretation would be to consider the kinetic energy degrees of freedom as a heat bath (the children throwing balls in my example).



#10
Mar2511, 03:38 PM

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No doubt the model is incomplete. What does regular mean?



#11
Mar2511, 03:45 PM

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If your "finite temperature ideal chain in outer space" really made sense as an object and had a force on it, then you'd have an argument that entropy is fundamental. In this case, would you be writing the powers that be, telling them that there are actually five fundamental interactions: gravity, EM, weak, strong, and entropy? Did the physics community really overlook this fifth force which acts on ideal chains in outerspace? If you want to go down this path, please tell me the physical setup that keeps this ideal chain at finite temperature, and tell me why your first law of thermodynamics is valid for the system. I think you're going to have a problem setting this up without using one of the four fundamental interactions of nature :). *disclaimer: there are people like Verlinde trying to get forces from entropy considerations. But this involves really vague arguments about "holographic screens" which are motivated from quantum considerations and black hole physics. Also, it doesn't work as far as I can tell :). 


#12
Mar2511, 04:32 PM

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#13
Mar2511, 07:43 PM

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But anyway there is content to my claim/belief that there is no sense in which an ideal chain (polymer if you like) can be sitting in vacuum and yet be at finite temperature. I'd like to settle this because if there really is a force on a polymer in outer space then I'd say we've discovered a new force of nature. I don't think the polymer can just fluctuate all on its own until it maximizes its entropythere has to be a force on it causing the fluctuations. Do you see what I mean? 


#14
Mar2611, 07:08 AM

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Then you include those magic words: "weakly coupled to a heat bath". Suddenly the polymer chain bunches up due to an "entropic force". But as must be, this motion is due to forces arising from the weak coupling to the bath that makes thermalization possible. Given this fact, the main interesting feature is that the resulting force at macroscopic scales is universal, independent of the detailed coupling and determined only by entropy or state counting for the ideal chain which we assume is essentially unchanged due to the weakness of the bath coupling. 


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Mar2611, 09:42 AM

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#16
Mar2611, 10:04 AM

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#17
Mar2611, 10:12 AM

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Thanks for all the help guys! 


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