[guga42k]

If somebody needs to build an intuition about entropy he could think about simple problem.

You are given insulated cylinder with a barrier in the middle. Left side of the cylinder filled with ideal gas A, and the right side filled with gas B. If given a particle one can distinguish A from B. The pressure and temperature on both sides are the same. Then you remove the barrier and gases mix. Question: how much work you need to do to revert the system into the original state? Hint: the work is equal to entropy difference between two states.

More generally, if you have proper insulated system and leave it be for a while. All of sudden you will have to do some work to come back to the original state despite energy conservation law holds.

[ithkuil]

If you need to do work in order to revert to the previous state, does it imply you can extract work when going to the first to the second state?

Given the scenario you just laid out it seems no work can be extracted just by letting mix two substances that are at the same temperature and pressure. But there is something about it that doesn't quite add up to my intuition of symmetry and conservation laws. Could you please elaborate more on that?

[Lichtso]

I think you can very well extract work from having a membrane and selectively let one substance mix into the other but not the other in the first [0]. It is called Osmosis [1].

[0]: https://en.wikipedia.org/wiki/Semipermeable_membrane [1]: https://en.wikipedia.org/wiki/Osmosis

[guga42k]

>If you need to do work in order to revert to the previous state, does it imply you can extract work when going to the first to the second state?

Nope. The work comes from the system coming from ordered state into unordered. Why the problem above is good for intuition because you can work out how to reverse the state. You invent semi-magical barrier which is fully transparent for particles A and reflects particles B, then you start to push such barrier from left to right up to the middle, compressing gas B (and making work!) and leave left part with gas A only, then repeat similar exercise on the right side.

>Given the scenario you just laid out it seems no work can be extracted just by letting mix two substances that are at the same temperature and pressure. But there is something about it that doesn't quite add up to my intuition of symmetry and conservation laws. Could you please elaborate more on that?

As far as I understand this asymmetry was the exact reason why entropy was introduced. Then later explained by Boltzmann via a measure of number of microscopic states.

Naturally second law of thermodynamics forbids perpetual engines.

[kuchenbecker]

Enter Maxwell's demon as a completely valid solution to this problem showing you can decrease entropy within that system (but you need to exclude the demon from the system).