Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature

TL;DR

This paper explores entropy production in a zero-temperature quantum optical cavity under continuous measurement, demonstrating that an effective inverse temperature regularizes divergence and linking it to information-theoretic bounds.

Contribution

It introduces the concept of an effective inverse temperature to define entropy production at zero temperature in quantum systems under continuous measurement.

Findings

Entropy production can be regularized at zero temperature using an effective inverse temperature.

A bound relates Fisher information, entropy production, and the effective inverse temperature.

There is a minimal entropy cost associated with acquiring information about quantum work.

Abstract

Fluctuation theorems allow one to make generalised statements about the behaviour of thermodynamic quantities in systems that are driven far from thermal equilibrium. In this article we use Crooks' fluctuation theorem to understand the entropy production of a continuously measured, zero-temperature quantum system; namely an optical cavity measured via homodyne detection. At zero temperature, if one uses the classical definition of inverse temperature $\beta$, then the entropy production becomes divergent. Our analysis shows that the entropy production can be well defined at zero temperature by considering the entropy produced in the measurement record leading to an effective inverse temperature $\beta_{\rm eff}$ which does not diverge. We link this result to the Cram\'er-Rao inequality and show that the product of the Fisher information of the work distribution with the entropy production is bounded below by half of the square of the effective inverse temperature $\beta_{\rm eff}$. This inequality indicates that there is a minimal amount of entropy production that is paid to acquire information about the work done to a quantum system driven far from equilibrium.