Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy

TL;DR

This paper introduces quantum ergodic channels with fixed points, analyzes their non-Markovian ergotropy dynamics, and proposes ergotropy backflow as an indicator of memory effects in quantum thermodynamics.

Contribution

It develops a theoretical framework for quantum ergodic channels, deriving Lindblad equations and linking non-Markovian ergotropy fluctuations to memory effects.

Findings

Ergotropy fluctuates and backflows in non-Markovian dynamics.

Markovian processes show monotonically decreasing ergotropy.

Ergotropy backflow can serve as a non-Markovianity indicator.

Abstract

In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy, a measure of the extractable work from a system under unitary evolution monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.