Trigger warning: the core of this question is more philosophical
Phenomena occur spontaneously because of two principles:
- Systems aim to minimize potential energy [1]
- Systems aim to maximize entropy
You can represent the conjunction of these two objectives (and why systems sometimes increase potential or decrease entropy) by means of thermodynamic potentials (Gibbs Free Energy and the like, which you aim to minimize)
(In Gibbs Free Energy, minus entropy times temperature represents a potential term, hence why increasing entropy 'decreases' this potential. The entropy term appears from the 1st/2nd law of thermodynamics, or dU = - dQ = -TdS)
My question is whether these representations (thermodynamic potentials) are correct by virtue of the fact that entropy and potential energy somehow fundamentally relate to the same thing, or if it's just a feature of mathematics/energy conservation.
I have a feeling that the principle of least action / potential minimization / entropy maximization are all flavours of the same property of the universe, but my knowledge is not super in depth on these.
[1] potential here as a source of spontaneous phenomena is more of a mental framework (this is how we speak of potentials, as that which generates motion) – potentials are representations of the cumulative effect of conservative force fields in a region of space, and it might be more proper to say the cause of said motion is the objects which generate the forces, curve spacetime, etc., not the potentials in themselves