Joint statistics of work and entropy production along quantum trajectories

TL;DR

This paper derives a comprehensive formula for the joint statistics of work and entropy production in driven quantum systems, revealing a quantum fluctuation theorem and a modified fluctuation-dissipation relation applicable to non-equilibrium steady-states.

Contribution

It introduces a general approach to compute joint work and entropy production statistics in quantum trajectories, extending classical thermodynamic relations to quantum systems.

Findings

Derived a joint cumulant generating function for work and entropy production.

Established a joint detailed fluctuation theorem under certain conditions.

Proposed a quantum fluctuation-dissipation relation incorporating quantum fluctuations.

Abstract

In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady-states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady-states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.