**A new improved 2nd law of thermodynamics**The 2nd law of thermodynamics says entropy increases. This is a powerful and useful idea, because you can

*compute* the entropy of different things, like different mixtures of chemicals, and use this idea to see which things can or cannot turn into which other things. But is the 2nd law always true? And if so, why?

People have studied this for over a century. It's clear by now that the 2nd law is only true under certain conditions... which happen to include the conditions we usually see around us. That's no coincidence. These are the situations that allow for life as we know it!

But the laws of physics allow for situations where entropy is very high and occasionally decreases for a short time, then comes back up... and also situations where entropy starts out high and

*decreases*.

In the second case, we can just stick a minus sign in our definition of time and save the 2nd law that way: now entropy

*increases*. The first situation can't be saved that way. And even in our universe, there will be tiny patches that work like this: if you've got a box of gas in equilibrium, there will be tiny patches where by random fluctuations, entropy decreases for a little while.

Can we prove

*theorems* saying that under certain precise conditions, the 2nd law of thermodynamics is true? Yes! Boltzmann did it a long time ago, and by now there are several theorems like this. These theorems are limited in their power - they haven't put an end to the mysteries surrounding the 2nd law. But they're useful because they let us see what's the logic behind the 2nd law, and where are the loopholes.

Theorems say "if X then Y". This doesn't mean Y is always true. It means that if you want Y to be false, you need X to be false too!

One loophole is that the 2nd law only applies to 'closed systems' - systems that don't interact with the rest of the world. You can lower the entropy of an 'open system' by transferring entropy to the rest of the world. That's what you're doing whenever you clean your room! That's what the guy in this cartoon should do.

My student

+Blake Pollard has a new paper where he generalizes the 2nd law to certain open systems called

**open Markov processes**. They're like random walks where the walkers can walk in and out of the room. Very roughly speaking, he shows that for these systems,

*entropy can only decrease if it flows out of the system*. But he's written a great blog article that explains it more clearly than I just did:

http://johncarlosbaez.wordpress.com/2014/02/16/relative-entropy-part-4/Check it out!