# Towards non-Hermitian quantum statistical thermodynamics

## TL;DR

This paper develops a framework for quantum statistical thermodynamics applicable to systems with non-Hermitian Hamiltonians that have real spectra, emphasizing entropy and equilibrium properties.

## Contribution

It introduces a novel thermodynamic formulation for non-Hermitian quantum systems with real eigenvalues, focusing on entropy and conserved quantities.

## Key findings

- Established entropy concepts for non-Hermitian systems
- Derived entropy inequalities in the non-Hermitian context
- Focused on equilibrium thermodynamics with conserved observables

## Abstract

Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems described by non-Hermitian Hamiltonians with real eigenvalues. We mainly focus on the case where the energy and another observable are the conserved quantities. The notion of entropy and entropy inequalities are central in our approach, which treats equilibrium thermodynamics.