Joint statistics of work and entropy production along quantum trajectories
arXiv:2011.11589 · doi:10.1103/PhysRevE.103.052138
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.
arXiv comment19 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
References in corpus (59)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- The role of quantum information in thermodynamics --- a topical review
- Open Quantum Systems. An Introduction
- Steady State Thermodynamics of Langevin Systems
- Three detailed fluctuation theorems
- Universal trade-off between power, efficiency, and constancy in steady-state heat engines
- Thermodynamic metrics and optimal paths
- Classical and Quantum Fluctuation Theorems for Heat Exchange
- The Three Faces of the Second Law: I. Master Equation Formulation
- Quantum Adiabatic Markovian Master Equations
- Fluctuation theorem uncertainty relation
- The Quantum Four Stroke Heat Engine: Thermodynamic Observables in a Model with Intrinsic Friction
- Thermodynamic uncertainty relations from exchange fluctuation theorems
- Fluctuation theorem for currents in open quantum systems
- Relaxation times of dissipative many-body quantum systems
- Entropy production and thermodynamic power of the squeezed thermal reservoir
- Irreversible work and inner friction in quantum thermodynamic processes
- Cycling tames power fluctuations near optimum efficiency
- Slow dynamics and thermodynamics of open quantum systems
- Metric adjusted skew information
- Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
- Entropy production along nonequilibrium quantum jump trajectories
- Covariance and Fisher information in quantum mechanics
- Optimal cycles for low-dissipation heat engines
- Quantum Operation Time Reversal
- Thermodynamic Geometry of Microscopic Heat Engines
- Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response
- Fluctuation theorems in driven open quantum systems
- Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production
- Thermodynamic length in open quantum systems
- Thermodynamic uncertainty relation in slowly driven quantum heat engines
- Work fluctuations in slow processes: quantum signatures and optimal control
- Distribution of work in isothermal non-equilibrium processes
- Nonequilibrium potential and fluctuation theorems for quantum maps
- Adiabatic response and quantum thermoelectrics for ac driven quantum systems
- Generators of Detailed Balance Quantum Markov Semigroups
- Optimal driving of isothermal processes close to equilibrium
- Geometric optimisation of quantum thermodynamic processes
- Fluctuation Relation for Quantum Heat Engines and Refrigerators
- Quantum work statistics close to equilibrium
- Quantum fluctuations hinder finite-time information erasure near the Landauer limit
- Analysis of slow transitions between nonequilibrium steady states
- Heat and work along individual trajectories of a quantum bit
- Fluctuation Relation for Heat Engines
- Entropy production and information fluctuations along quantum trajectories
- Statistical properties of entropy production derived from fluctuation theorems
- Unifying approach for fluctuation theorems from joint probability distributions
- Geometry of work fluctuations versus efficiency in microscopic thermal machines
- Work and entropy production in generalised Gibbs ensembles
- Equivalent definitions of the quantum nonadiabatic entropy production
- Geometric magnetism in open quantum systems
- Energetic footprints of irreversibility in the quantum regime
- Quantum jump approach to microscopic heat engines
- Work fluctuation-dissipation trade-off in heat engines
- Calculating work in weakly driven quantum master equations: backward and forward equations
- Role of work in matter exchange between finite quantum systems
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