# Is an entropic force an actual force that can be explained as a fundamental interaction?

Fundamental interactions, such as electromagnetism, the strong force, the weak force, and possibly gravitation, all have something in common: They can be described in terms of relativistic quantum fields, and are clearly the results of interactions between two different kinds of fields. For example, with an electron interacting via the electromagnetic force, one can describe the electromagnetic field using quantum electrodynamics, and an equation of motion can be obtained from the QED lagrangian: $$\mathcal{L}_{QED} = \bar{\psi} (i \gamma^{\mu} D_{\mu} - m)\psi - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$ And, the interaction picture here is clear: The electron field ($\psi$) interacts with the electromagnetic field, resulting in its change in motion.

However, with an entropic force (such as the elasticity of a polymer), can the same be done? Can one construct a Lagrangian for the elastic force of a polymer, and is there some sort of "entropy force field" that can act as the relativistic quantum field with which polymer molecules interact? Or is the entropic force not a force at all, just a consequence of the universe tending towards maximum entropy? Or, alternatively, is it possible that every entropic force that exists in this universe is actually a manifestation of one of the fundamental forces (electromagnetism, strong force, weak force, gravity), meaning that the elastic force in a polymer is really something like electromagnetic interaction?

• I think that's the kind of reasoning that motivates the Rayleight dissipation function, but I'm not sure right now. Usually entropic/thermodynamic forces are motivated fenomenologically, and not through first principles. – Hydro Guy Nov 11 '13 at 11:41

Entropic forces are emergent effects resulting from systems tending towards maximum entropy. Such emergent effects can be described as forces in an effective theory giving a coarse-grained system description ignoring the entropic degrees of freedom.

An extremely simple example (Mikado model) demonstrating the emergence of an $1/r^2$ Entropic force is given here:

http://www.science20.com/hammock_physicist/it_bit_entropic_gravity_pedestrians-66244 In this, and many other examples, an entropic attractive force emerges in a system with no other interactions than excluded volume effects. So it is not correct to claim "that every entropic force is the manifestation of one of the fundamental forces".

• The excluded volume effect exists because of electromagnetism (primarily). Without electromagnetism, objects would pass through each other. So I don't see how this is a counterexample to the claim "Every entropic force is the manifestation of one of the fundamental forces". – Steve Byrnes Nov 13 '13 at 17:05
• Are you referring to the Mikado model? You need more than a lot of imagination to claim this model contains an electromagnetic interaction. – Johannes Nov 14 '13 at 16:08
• @SteveB - if you mean that in trivial systems void of any interactions between its constituents, no entropic force can emerge, I am with you. However, to claim you need one of the four fundamental forces is not correct. – Johannes Nov 14 '13 at 16:25
• If you take away electromagnetic force, and strong, and weak, and gravity, then what's left? I'll tell you what's left: "A trivial system void of any interactions between its constituents". And we both agree that such a system has no entropic forces. Therefore "You need at least one of the four fundamental forces." Right? A lot of people get the confused idea that the "four fundamental forces" is not a complete list of fundamental forces, and we should include other forces along with those four. Please don't encourage that misperception! – Steve Byrnes Nov 14 '13 at 17:01
• @SteveB - OP wants to know if entropic forces are the manifestation of a particular fundamental force (EM or otherwise). The answer is "no". Entropic forces emerge in hypothetical model systems with rudimentary (excluded volume) interactions. – Johannes Nov 15 '13 at 14:53

Entropy exists on all systems including elasticity in polymers. I'm not sure but in most polymers the molecules are held together by hydrogen bonds. You might be able to count the bonds and then add the numbers and use it as an electron charge field equation.

Many physicists have argued (succesfuly?) about this. Now the concept (and content) of conventional force can be discussed, the fact remains that entropy in one way or another is there and one can formulate the formalism around this (or even beyond..).

A similar (and related?) concept is that of an inertial force (and inertia itself). There are many interesting connections between these concepts and their interplay (previous link on entropic forces has some links in this direction also).

For example using concepts from information geometry and maximum entropy, Newtonian dynamics can be produced (or emerge if you like)

At the end of the day it can be around what one whould like to call fundamental (or more correctly "assigned") force or property..

There is in fact a literature on using concepts of emergent phenomena in physics (especially lately)

Finaly one should take account of phenomena (e.g like the Aharonov-Bohm effect), which are not "assigned" in the conventional sense (the potential is not observable or assignable in this way)..

Infact entropic force must be even more fundamental than other forces. and other forces are emergent results of entropic force.

• Why 'must' this be so? – Neuneck Jan 12 '14 at 20:14
• @Neuneck, many physicists have argued (succesively) about this. Now the concept (and content) of conventional force can be discussed, the fact remains that entropy in one eay or another is there and one can formulate the formalism around this (and even beyond) – Nikos M. Jun 20 '14 at 19:45
• @Neuneck, a similar (and related?) concept is that of an inertial force, imo there are many interesting things between these concepts and their interplay – Nikos M. Jun 20 '14 at 19:46