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

August 23, 2015

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.

Keywords:

thermal states, thermal quantum field theory, local thermal equilibrium, KMS condition