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

##### 1 Answer

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

Or the two following equations:

#DeltaS_("univ","tot")(T,P,V,n_i,n_j, . . . , n_N) > 0# #DeltaS_("univ")(T,P,V,n_i,n_j, . . . , n_N) >= 0#

where we differentiate between

total entropy of the universeand the stagnancy or increase inentropy of the universe due toasingleisolated 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) *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.