Non-hermitian quantum thermodynamics

TL;DR

This paper investigates the validity of quantum thermodynamic relations in non-Hermitian systems, demonstrating the Jarzynski equality's applicability and proposing experimental setups to test these theoretical predictions.

Contribution

It shows that the Jarzynski equality holds for all non-Hermitian quantum systems with real spectra and extends thermodynamic bounds to systems with complex conjugate eigenenergies.

Findings

Jarzynski equality applies to non-Hermitian systems with real spectra

Carnot bound holds even with complex eigenenergies in conjugate pairs

Proposed experimental setups in microcavities and tight-binding models

Abstract

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions. Namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.