# Eternal life of entropy in non-Hermitian quantum systems

## TL;DR

This paper introduces a framework for analyzing Von Neumann entropy in non-Hermitian quantum systems, revealing distinct entropy behaviors depending on PT symmetry status, including decay, revival, and eternal life.

## Contribution

It develops a new approach to define and study Von Neumann entropy in non-Hermitian systems, especially in PT symmetric regimes, with novel insights into entropy dynamics.

## Key findings

- Entropy decays rapidly to zero in unbroken PT symmetry
- At the exceptional point, entropy decays asymptotically to zero
- Broken PT symmetry leads to entropy approaching a finite constant (eternal life)

## Abstract

We find a new effect for the behaviour of Von Neumann entropy. For this we derive the framework for describing Von Neumann entropy in non-Hermitian quantum systems and then apply it to a simple interacting PT symmetric bosonic system. We show that our model is well defined even in the PT broken regime with the introduction of a time-dependent metric and that it displays three distinct behaviours relating to the PT symmetry of the original time-independent Hamiltonian. When the symmetry is unbroken, the entropy undergoes rapid decay to zero (so-called "sudden death") with a subsequent revival. At the exceptional point it decays asymptotically to zero and when the symmetry is spontaneously broken it decays asymptotically to a finite constant value ("eternal life").