Entropy production and asymptotic factorization via thermalization: a collisional model approach

TL;DR

This paper investigates entropy production in open quantum systems using a collisional model, showing that the environment's entropy bounds are asymptotically saturated and the system factorizes at equilibrium.

Contribution

It introduces a collisional model approach to analyze entropy bounds and demonstrates asymptotic factorization and equilibrium in open quantum systems.

Findings

The extrinsic entropy bound is asymptotically saturated at large interaction times.

The system reaches an equilibrium state that factorizes from the environment.

Analytical proof of factorization in strong coupling and numerical analysis in weak coupling regimes.

Abstract

The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environment degrees of freedom. Starting from these premises, we analyze the entropy variation of an open quantum system in terms of two distinct relations: the Clausius inequality, that provides an intrinsic bound for the entropy variation in terms of the heat absorbed by the system, and an extrinsic inequality, which instead relates the former to the corresponding entropy increment of the environment. By modeling the thermalization process with a Markovian collisional model, we compare and discuss the two bounds, showing that the latter is asymptotically saturated in the limit of large interaction time. In this regime not only the reduced density matrix of the system reaches an equilibrium configuration, but it also factorizes from the environment degrees of freedom. This last result is proven analytically when the system-bath coupling is sufficiently strong and through numerical analysis in the weak-coupling regime.