I’ve posted a new article in the physics for mathematicians series. I’m working on finishing an article for that series about thermodynamics and statistical mechanics, but I’m not done with that one yet. The piece I’ve just finished is on a sort of side question that comes up a lot when learning about thermodynamics: how is it possible for anything like the laws of thermodynamics, which have entropy increasing in only one time direction, to arise from completely time-symmetric microscopic laws of physics? This article explores this question through a toy model which exhibits the same sort of behavior but for which all the relevant computations can be done exactly.
This article is a lot more accessible than the rest of the “physics for mathematicians” series! Anyone with an understanding of the expected value and the variance of a random variable should be totally fine. I felt like this model did a lot for my understanding of the question when I first learned about it, and I hope it can be helpful for you too.