Temperature in Nonequilibrium Quantum Systems

TL;DR

This paper proposes a method to define and assign a meaningful temperature to general nonequilibrium quantum systems using a thermodynamic framework based on observables and entropy derivatives.

Contribution

It introduces a novel way to define temperature in nonequilibrium quantum systems through a thermodynamic approach involving entropy and internal energy.

Findings

Temperature can be assigned to nonequilibrium quantum states.

The defined temperature is positive for passive states.

Subsystems can have different temperatures even in a global thermal state.

Abstract

We extend on ideas from standard thermodynamics to show that temperature can be assigned to a general nonequilibrium quantum system. By choosing a physically motivated complete set of observables and expanding the system state thereupon, one can read a set of relevant, independent thermodynamic variables which include internal energy. This expansion allows us to read a nonequilibrium temperature as the partial derivative of the von Neumann entropy with respect to internal energy. We show that this definition of temperature is one of a set of thermodynamics parameters unambiguously describing the system state. It has appealing features such as positivity for passive states and consistency with the standard temperature for thermal states. By attributing temperature to correlations in a bipartite system, we obtain a universal relation which connects the temperatures of subsystems, total system as a whole, and correlation. All these temperatures can be different even when the composite system is in a well-defined Gibbsian thermal state.