Statistical mechanics

Summary

Statistical mechanics derives the large-scale behaviour of matter from the laws that govern its many small parts. It replaces the exact state of all particles, the microstate, by a probability distribution over microstates, a statistical ensemble. Thermodynamic quantities such as energy, pressure and entropy then become averages or functionals of this distribution. Its mathematics joins probability, measure theory, combinatorics and operator algebras. It also supplies models, such as the Ising model, that are studied for their own sake.