Instability of Equilibrium States for Coupled Heat Reservoirs at Different Temperatures

TL;DR

This paper demonstrates that quantum systems coupled to two reservoirs at different temperatures generally lack equilibrium states, especially when temperature differences are significant, using spectral analysis of the system's generators.

Contribution

It provides a rigorous spectral analysis showing the absence of equilibrium states in open quantum systems with reservoirs at different temperatures.

Findings

No equilibrium states normal with respect to decoupled systems at different temperatures.

Spectral analysis of quantum Liouville operators reveals instability of equilibrium.

Results hold when temperature differences are not too small.

Abstract

We consider quantum systems consisting of a ``small'' system coupled to two reservoirs (called open systems). We show that such a system has no equilibrium states normal with respect to any state of the decoupled system in which the reservoirs are at different temperatures, provided that either the temperatures or the temperature difference divided by the product of the temperatures are not too small. Our proof involves an elaborate spectral analysis of a general class of generators of the dynamics of open quantum systems, including quantum Liouville operators (``positive temperature Hamiltonians'') which generate the dynamics of the systems under consideration.