Thermodynamic consistency of the optomechanical master equation

TL;DR

This paper examines the thermodynamic consistency of different master equations in optomechanical systems and finds that only a global description of baths ensures compliance with the second law of thermodynamics.

Contribution

It demonstrates that local and dressed-state master equations violate thermodynamic principles, advocating for a global approach for consistency.

Findings

Local and dressed-state master equations violate the second law under certain conditions.

Global master equation maintains thermodynamic consistency.

Weak coupling regime favors the global description.

Abstract

We investigate the thermodynamic consistency of the master equation description of heat transport through an optomechanical system attached to two heat baths, one optical and one mechanical. We employ three different master equations to describe this scenario: (i) The standard master equation used in optomechanics, where each bath acts only on the resonator that it is physically connected to; (ii) the so-called dressed-state master equation, where the mechanical bath acts on the global system; and (iii) what we call the global master equation, where both baths are treated non-locally and affect both the optical and mechanical subsystems. Our main contribution is to demonstrate that, under certain conditions including when the optomechanical coupling strength is weak, the second law of thermodynamics is violated by the first two of these pictures. In order to have a thermodynamically consistent description of an optomechanical system, therefore, one has to employ a global description of the effect of the baths on the system.