KMS state

Summary

A KMS state is a state on a C*-algebra with a time evolution that satisfies the Kubo–Martin–Schwinger condition at an inverse temperature $\beta$. It is the definition of a thermal equilibrium state for infinite quantum systems, where the Gibbs density $e^{-\beta H} / \tr e^{-\beta H}$ makes no sense. For a finite quantum system the KMS state is exactly the Gibbs state. Several KMS states at the same $\beta$ signal a phase transition.