Joint statistics of work and entropy production along quantum trajectories

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.

19 pages, 1 figure. The results presented here have been adapted from a previous draft of arXiv:2006.07316, which has now been divided into two articles

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• Probing coherent quantum thermodynamics using a trapped ion
• Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Time-resolved Stochastic Dynamics of Quantum Thermal Machines
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware
• Information geometry of transitions between quantum nonequilibrium steady states
• Artificially intelligent Maxwell's demon for optimal control of open quantum systems
• Finite-time bounds on the probabilistic violation of the second law of thermodynamics
• Quantum thermodynamics under continuous monitoring: a general framework