Joint statistics of work and entropy production along quantum trajectories

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, then 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.

Automated summary

This study focuses on the joint statistics of work and entropy production in driven quantum systems, deriving a general formula for the cumulant generating function and the detailed fluctuation theorem along with a modified fluctuation-dissipation relation. It shows that as long as the driven system remains close to the instantaneous Gibbs state, these relations hold true, even in systems that violate detailed balance.