Work statistics in non-Hermitian evolutions with Hermitian endpoints

TL;DR

This paper introduces a modified two-point measurement method to analyze work statistics in non-Hermitian quantum systems with Hermitian endpoints, revealing key differences from Hermitian systems.

Contribution

It develops a new measurement approach applicable to non-Hermitian systems with Hermitian initial and final states, bridging a gap in quantum thermodynamics analysis.

Findings

The method reduces to the standard in Hermitian cases.

Work statistics differ significantly between non-Hermitian and Hermitian systems.

Application to the non-Hermitian Su-Schrieffer-Heeger model demonstrates the method's effectiveness.

Abstract

Non-Hermitian systems with specific forms of Hamiltonians can exhibit novel phenomena. However, it is difficult to study their quantum thermodynamical properties. In particular, the calculation of work statistics can be challenging in non-Hermitian systems due to the change of state norm. To tackle this problem, we modify the two-point measurement method in Hermitian systems. The modified method can be applied to non-Hermitian systems which are Hermitian before and after the evolution. In Hermitian systems, our method is equivalent to the two-point measurement method. When the system is non-Hermitian, our results represent a projection of the statistics in a larger Hermitian system. As an example, we calculate the work statistics in a non-Hermitian Su-Schrieffer-Heeger model. Our results reveal several differences between the work statistics in non-Hermitian systems and the one in Hermitian systems.