Stochastic entropy production for continuous measurements of an open quantum system

TL;DR

This paper studies the stochastic entropy production in a two-level quantum system under measurement protocols, revealing how entropy production indicates irreversibility and satisfies fluctuation theorems during quantum measurement processes.

Contribution

It introduces a stochastic model for entropy production in open quantum systems under measurement, connecting quantum measurement dynamics with thermodynamic irreversibility.

Findings

Entropy production vanishes at equilibrium with constant coupling.

Time-dependent coupling results in positive entropy production, indicating irreversibility.

The entropy production obeys a detailed fluctuation theorem during measurement protocols.

Abstract

We investigate the total stochastic entropy production of a two-level bosonic open quantum system under protocols of time dependent coupling to a harmonic environment. These processes are intended to represent the measurement of a system observable, and consequent selection of an eigenstate, whilst the system is also subjected to thermalising environmental noise. The entropy production depends on the evolution of the system variables and their probability density function, and is expressed through system and environmental contributions. The continuous stochastic dynamics of the open system is based on the Markovian approximation to the exact, noise-averaged stochastic Liouville-von Neumann equation, unravelled through the addition of stochastic environmental disturbance mimicking a measuring device. Under the thermalising influence of time independent coupling to the environment, the mean rate of entropy production vanishes asymptotically, indicating equilibrium. In contrast, a positive mean production of entropy as the system responds to time dependent coupling characterises the irreversibility of quantum measurement, and a comparison of its production for two coupling protocols, representing connection to and disconnection from the external measuring device, satisfies a detailed fluctuation theorem.