Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics

TL;DR

This paper develops a master equation for open quantum systems with a finite, evolving bath, capturing nonequilibrium dynamics and correlations, and establishes a thermodynamic framework applicable to nanoscale quantum devices.

Contribution

It introduces a novel master equation that accounts for system-bath correlations and a dynamically evolving bath, extending the analysis of nonequilibrium quantum thermodynamics.

Findings

Good agreement with exact evolution where traditional methods fail

Stable negative temperature states can coexist with Boltzmann entropy

Framework applicable to quantum engines and refrigerators

Abstract

Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when the memory effects cannot be disregarded. Here, we derive a master equation that explicitly accounts for system-bath correlations and includes, at a coarse-grained level, a dynamically evolving bath. Such a master equation applies to a wide variety of physical systems including those described by Random Matrix Theory or the Eigenstate Thermalization Hypothesis. We obtain a local detailed balance condition which, interestingly, does not forbid the emergence of stable negative temperature states in unison with the definition of temperature through the Boltzmann entropy. We benchmark the master equation against the exact evolution and observe a very good agreement in a situation where the conventional Born-Markov-secular master equation breaks down. Interestingly, the present description of the dynamics is robust and it remains accurate even if some of the assumptions are relaxed. Even though our master equation describes a dynamically evolving bath not described by a Gibbs state, we provide a consistent nonequilibrium thermodynamic framework and derive the first and second law as well as the Clausius inequality. Our work paves the way for studying a variety of nanoscale quantum technologies including engines, refrigerators, or heat pumps beyond the conventionally employed assumption of a static thermal bath.