What is the nature of entropy and its relationship to equilibrium?

[funcosed]

Homework Statement

My understanding of entropy seems to be a bit flawed. I think of it as disorder. As an example consider a bag with a layer of salt in the bottom and a layer of pepper on top. If the bag is shaken the salt and pepper mix (move to higher entropy) and no matter how much you shake you won't reproduce the original state.
My problem with this is if there is a density difference once you stop shaking the bag it will return to the original state or something close to it, after enough time. For instance try the same experiment with oil and water.
The problem is probably that I only have a basic understanding of these things, so what's the real story?

Homework Equations

The Attempt at a Solution

 

[Zacku]

Hi,

The problem is that you try to apply the second principle of thermodynamics for the thermodynamic entropy to a configurational entropy for a binary mixture of macroscopic grains.

There is no reason for your extension of the second principle to be true in general even though statistical mechanics of powders is something very appealing if achievable and therefore many effort are done in this direction since few decades.

The fundamental reasons why your reasoning may not work in general is that the way your powders arrange themselves when you shake them is protocol dependent and most likely even on days time scale the final result has still a memory of the original state. Moreover your system is dissipative and hence do not conserve probability (at least not in the sense of Liouville Theorem).