# What is the Second law of thermodynamics. How would you express it mathematically?

Oct 20, 2016

It simply says that the total entropy of the universe always increases in some way, somewhere, as time passes.

Or the two following equations:

• $\Delta {S}_{\text{univ","tot}} \left(T , P , V , {n}_{i} , {n}_{j} , . . . , {n}_{N}\right) > 0$
• $\Delta {S}_{\text{univ}} \left(T , P , V , {n}_{i} , {n}_{j} , . . . , {n}_{N}\right) \ge 0$

where we differentiate between total entropy of the universe and the stagnancy or increase in entropy of the universe due to a single isolated process.

$T$, $P$, $V$, and $n$ are typical Ideal Gas Law variables.

This is because certain natural processes are irreversible, and as such, work/have worked to increase the total entropy of the universe in such a way that a corresponding reverse process doesn't undo the increase in entropy.

Note that (non-total) $\Delta {S}_{\text{univ}}$ can be $0$ for a single isolated reversible process that isn't exposed to the universe. Despite that, the entropy of the (entire, total) universe itself will increase due to some other process in some other part of the world.