Excess entropy production in quantum system: Quantum master equation approach

TL;DR

This paper investigates excess entropy production in open quantum systems described by quantum master equations, proposing a new approach using full counting statistics and Berry-Sinitsyn-Nemenman vectors to analyze nonequilibrium steady states.

Contribution

It introduces a novel method to quantify excess entropy production in quantum systems using QME and full counting statistics, connecting it to Berry phase concepts.

Findings

Excess entropy production reduces to von Neumann entropy difference under certain conditions.

The BSN vector describes entropy production in the weakly nonequilibrium regime.

Classical and quantum entropy production expressions differ but are approximately equivalent in weakly nonequilibrium regimes.

Abstract

For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by $\ln \breve{\rho}_0$ and $\rho_0$ where $\rho_0$ is the instantaneous steady state of the QME and $\breve{\rho}_0$ is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.