Entropy production and non-Markovian dynamical maps

TL;DR

This paper investigates how non-Markovian quantum dynamics challenge the traditional understanding of entropy production and the second law of thermodynamics, emphasizing the need to include environment contributions explicitly.

Contribution

It demonstrates that standard entropy production can be negative in non-Markovian dynamics, highlighting the importance of environment entropy in thermodynamic consistency.

Findings

Entropy production can be negative for non-Markovian maps.

Absence of semigroup property affects the stationarity of thermal states.

Environment contributions are essential for a consistent second law.

Abstract

In the weak-coupling limit approach to open quantum systems, the presence of the bath is eliminated and accounted for by a master equation that introduces dissipative contributions to the system reduced dynamics. Within this framework, there are no bath entropy contributions to the entropy balance. We show that, as a consequence, the entropy production fails to be positive for a class of physically legitimate (i.e., completely positive and trace preserving) non-Markovian dynamical maps. Moreover, in the absence of the semigroup property, if the reduced dynamics has a thermal asymptotic state, this need not be stationary. In this case, even the integrated entropy production becomes negative. These observations imply that, when the conditions leading to reduced dynamics of semigroup type are relaxed, a consistent formulation of the second law of thermodynamics requires that the environment contribution to the entropy balance be explicitly taken into account.