TITLE: What are entropic forces and how are they related to free energy minimization?
QUESTION [0 upvotes]: Are entropic forces only a result of "entropy maximization" (for isolated systems) and "free energy minimization"(for systems in equilibrium)?
Can we think of phase transitions as a result of "entropic forces"?

REPLY [1 votes]: short answer: yes.
Entropic forces are "effective" forces that spawn out of entropy maximization: if your system is a in a low entropy state and can evolve into a higher-entropy one, there will be a push ("force") towards a higher entropy state. Interestingly, this can arise even in the absence of long-range interaction between particles. The reason is that the free energy contains an entropy-term which can give rise, upon derivation, to a force.
The simples example is that of a hard-sphere gas: if you mix together spheres that can not intersect with each other (they are "hard") and if the concentration is high enough, spheres will undergo a phase separation from a disordered state to a crystalline one, the crystal one being (counter-intitively!) the maximum-entropy one.
However, the free energy also contains an energy term: phase transitions are always a balance between entropic and energetic effects, and you can not in general attribute them to only one of the two, although some examples in which the leading term is purely entropic exists (hard sphere, nematic transition, etc.).
If you have a strong enough energy contribution, you can fight entropy. So energy must always be taken into account.
Here some further references which you can navigate to reach the level of description that suits you best:

a recent paper "extending" the concept of entropic force
the wiki page for entropic forces , zoomed in in the section about depletion force (another common example and a widely used experimental tool)
a review on entropy in self-assembly processes, including all the math you probably need.
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