Gibbs measure

Summary

A Gibbs measure is a probability measure in which the weight of a configuration is proportional to $e^{-\text{energy}}$. It comes from statistical mechanics, where it describes a system in thermal equilibrium. In dynamics, the thermodynamic formalism uses Gibbs measures on shift spaces. There the measure of a cylinder of length $n$ is comparable to the exponential of a Birkhoff sum of a potential. For a Hölder potential on a mixing subshift of finite type the Gibbs measure is unique and is the equilibrium state of the potential.