Weighted Detailed Balance and Local KMS Condition for Non-Equilibrium Stationary States : Dedicated to the memory of Shuichi Tasaki(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Abstract

We give a general definition of the local KMS condition and we prove its equivalence with a nonlinear Gibbs prescription. We discuss the irreversible (H, β)-KMS condition, its connections with the local KMS condition and we study the irreversible (H, β)-KMS condition for Markov generators of stochastic limit type. We introduce a definition of weighted detailed balance based on the notion of current decomposition and discuss invariant states with constant micro-currents. As an example, we construct a non-equilibrium steady state for a quantum spin chain coupled to two reservoirs at different temperatures and study its cycle dynamics and entropy production.