Local master equations may fail to describe dissipative critical behavior

Abstract

Local quantum master equations provide a simple description of interacting subsystems coupled to different reservoirs. They have been widely used to study nonequilibrium critical phenomena in open quantum systems. We here investigate the validity of such a local approach by analyzing a paradigmatic system made of two harmonic oscillators each in contact with a heat bath. We evaluate the steady-state mean occupation number for varying temperature differences and find that local master equations generally fail to reproduce the results of an exact quantum-Langevin-equation description. We relate this property to the inability of the local scheme to properly characterize intersystem correlations, which we quantify with the help of the quantum mutual information.