Proper effective temperature of nonequilibrium steady state

Abstract

We define a proper effective temperature for relativistic nonequilibrium steady states (NESSs). A conventional effective temperature of NESSs is defined from the ratio of the fluctuation to the dissipation. However, NESSs have relative velocities to the heat bath in general, and hence the conventional effective temperature can be frame-dependent in relativistic systems. The proper effective temperature is introduced as a frame-independent (Lorentz-invariant) quantity that characterizes NESSs. We find that the proper effective temperature of NESSs is higher than the proper temperature of the heat bath in a wide range of holographic models even when the conventional effective temperature is lower than the temperature of the heat bath.