Statistical Mechanics: A Selective Review of Two Central Issues

TL;DR

This paper provides a selective overview of how statistical mechanics explains the emergence of time asymmetry and phase transitions in macroscopic systems, emphasizing their collective nature and mathematical formulations.

Contribution

It highlights the mathematical formulations of emergent phenomena like time asymmetry and phase transitions in the context of large scale ratios in statistical mechanics.

Findings

Explains microscopic origins of macroscopic time asymmetry.

Describes mathematical formalism of phase transitions.

Highlights emergent collective properties in statistical mechanics.

Abstract

I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These phenomena are emergent collective properties not discernible in the behavior of individual atoms. They are given precise and elegant mathematical formulations when the ratio between macroscopic and microscopic scales becomes very large.