Ergodic theory, entropy and application to statistical mechanics
UChicago Math REU, 2019
This is an expository paper after 8 weeks of studying at the Mathematics Research Experience for Undergraduates @ UChicago.
Ergodic theory originated in statistical mechanics. This paper first introduces the ergodic hypothesis, a fundamental problem in statistical mechanics. In order to come up with a solution, this paper explores some basic ideas in ergodic theory. Next, the paper defines measure-theoretical entropy and shows its connection to physical entropy. Lastly, these results are used to construct Gibbs ensembles, a useful tool in statistical mechanics.