Non-Markovianity through entropy-based quantum thermodynamics

TL;DR

This paper proposes a novel entropy-based thermodynamic approach to quantify non-Markovianity in quantum dynamical maps, linking heat flow, quantum coherence, and non-Markovian behavior, with applications to various quantum processes.

Contribution

It introduces a heat flow-based measure of non-Markovianity using entropy in quantum thermodynamics, applicable to unital and certain non-unital quantum maps, connecting thermodynamics with quantum coherence.

Findings

The measure detects non-Markovianity via heat flow analysis.

It applies to unital quantum maps and can extend to other thermodynamic functions.

The approach aligns with quantum coherence measures in quantum processes.

Abstract

We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown of monotonicity of thermodynamic functions. By adopting an entropy-based formulation of quantum thermodynamics, we use the relationship between heat and entropy to propose a measure of non-Markovianity based on the heat flow for single-qubit quantum evolutions. This measure can be applied for unital dynamical maps that do not invert the sign of the internal energy. Under certain conditions, it can also be extended for other thermodynamic functions, such as internal energy and work flows. In this context, a natural connection between heat and quantum coherence can be identified for dynamical maps that are both unital and incoherent. As applications, we explore dissipative and non-dissipative quantum dynamical processes, illustrating the compatibility between our thermodynamic quantifiers and the well-establish measure defined via quantum coherence.