What is statistical mechanics?

Abstract

Statistical mechanics explains the simple behavior of complex systems. It works by studying not a particular instance, but the typical behavior of a large collection (or ensemble) of systems, which is far easier to calculate. Entropy, free energies, order parameters, phases and phase transitions emerge as collective behaviors that are not manifest in the complex microscopic laws. This text will develop the statistical mechanical machinery needed to generate the new laws governing these emergent behaviors. Exercises in this chapter discuss emergence, Stirling’s formula, random matrix theory, small world networks, an NP complete problem, active matter, and topics in statistics.