Quantum entropy of systems described by non-Hermitian Hamiltonians

TL;DR

This paper extends the concept of quantum entropy to systems with non-Hermitian Hamiltonians, providing a framework to describe irreversibility and information flow in dissipative quantum systems.

Contribution

It introduces a generalized von Neumann entropy for non-Hermitian systems, incorporating normalized and non-normalized density operators to capture irreversible processes.

Findings

Generalized entropy monitors disorder in dissipative systems

Normalized and non-normalized density operators are essential for non-Hermitian entropy

Application to simple models like two-level tunneling systems

Abstract

We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning.