Fluctuation relation for heat exchange in Markovian open quantum systems

TL;DR

This paper derives a fluctuation relation for heat exchange in open quantum systems under Markovian dynamics, revealing exponential suppression of second law violations with increasing heat and temperature differences.

Contribution

It introduces a fluctuation relation specific to quantum heat exchange in Markovian open systems, linking probabilities of forward and reverse heat transfer processes.

Findings

Probability ratio of heat absorption and release follows an exponential relation.

Violations of the second law decrease exponentially with heat and temperature differences.

The relation provides insights into thermodynamic fluctuations at the quantum level.

Abstract

A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability of that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. We also argue that the probability of the violation of the second law of thermodynamics (here in the form of net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences.