KMS-like Properties of Local Equilibrium States in Quantum Field Theory

TL;DR

This paper introduces the Local KMS (LKMS) condition as a local thermal equilibrium criterion in quantum field theory, showing its equivalence to the LTE condition and extending the concept of thermal states to out-of-equilibrium scenarios.

Contribution

It establishes the LKMS condition as a local generalization of the KMS condition, linking it to the LTE condition and broadening the understanding of local thermal states in quantum fields.

Findings

LKMS condition is equivalent to LTE condition for Klein-Gordon states.

Known LTE states satisfy the LKMS condition with spatially and temporally varying temperature.

The framework extends to mixed-temperature LKMS and LTE states.

Abstract

A new condition, called "Local KMS Condition", characterizing states of a quantum field to which one can ascribe, at a given spacetime point, a temperature, is introduced in this article. It will be shown that the Local KMS Condition (LKMS condition) is equivalent to the Local Thermal Equilibrium (LTE) condition, proposed previously by Buchholz, Ojima and Roos, for states of the quantized scalar Klein-Gordon field that fulfill the analytic microlocal spectrum condition. Therefore, known examples of states fulfilling the LTE condition provide examples of states obeying the LKMS condition with a temperature distribution varying in space and time. The results extend to the generalized cases of mixed-temperature LKMS and LTE states. The LKMS condition therefore provides a promising generalization of the KMS condition, which characterizes global thermal equilibrium states with respect to an inertial time evolution, to states which are globally out of equilibrium but still possess a local temperature distribution.