Comparison of work fluctuation relations

Abstract

We compare two predictions regarding the microscopic fluctuations of a system that is driven away from equilibrium: one due to Crooks [J. Stat. Phys. 90, 1481 (1998)] which has gained recent attention in the context of nonequilibrium work and fluctuation theorems, and an earlier, analogous result obtained by Bochkov and Kuzovlev [Zh. Eksp. Teor. Fiz. 72(1), 238247 (1977)]. Both results quantify irreversible behavior by comparing probabilities of observing particular microscopic trajectories during thermodynamic processes related by time-reversal, and both are expressed in terms of the work performed when driving the system away from equilibrium. By deriving these two predictions within a single, Hamiltonian framework, we clarify the precise relationship between them, and discuss how the different definitions of work used by the two sets of authors gives rise to different physical interpretations. We then obtain a extended fluctuation relation that contains both the Crooks and the Bochkov-Kuzovlev results as special cases.

14 pages with 1 figure, accepted for publication in the Journal of Statistical Mechanics

References in corpus (12)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• The Nonequilibrium Thermodynamics of Small Systems
• Stochastic thermodynamics: Principles and perspectives
• Rare events and the convergence of exponentially averaged work values
• Fluctuation Theorems
• Comparison of far-from-equilibrium work relations
• Fluctuation and dissipation of work in a Joule experiment

Cited by in corpus (39)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Thermodynamics with continuous information flow
• Thermodynamic costs of information processing in sensory adaption
• Finite quantum dissipation: the challenge of obtaining specific heat
• Thermodynamic control -- an old paradigm with new applications
• Conservation Laws and Work Fluctuation Relations in Chemical Reaction Networks
• Optimal Control of Overdamped Systems
• Role of External Flow and Frame Invariance in Stochastic Thermodynamics
• Fluctuations in heat engines
• Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
• Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
• Comment on: Failure of the Work-Hamiltonian Connection for Free-Energy Calculations [Phys Rev Lett 100, 020601 (2008), arXiv:0704.0761]
• Fluctuation, Dissipation and the Arrow of Time
• Free energy reconstruction from steered dynamics without post-processing
• Stochastic thermodynamics of relativistic Brownian motion
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Quantum mechanical work
• Fluctuation theorems and inequalities generalizing the second law of thermodynamics off equilibrium
• Vanishing efficiency of speeded-up quantum Otto engines
• Waste-recycling Monte Carlo with optimal estimates: application to free energy calculations in alloys
• Exact Nonequilibrium Work Generating Function for a Small Classical System
• Jarzynski equality for conditional stochastic work
• Quantum work: Reconciling quantum mechanics and thermodynamics
• Fluctuation relations: a pedagogical overview
• Tsallis statistics generalization of non-equilibrium work relations
• Thermodynamics as a nonequilibrium path integral
• Statistics of work done in degenerate parametric amplification process
• Fluctuation theorems for genuine quantum mechanical regimes
• Nonequilibrium work equalities in isolated quantum systems
• Fluctuation relation in continuous-time random walks driven by an external field
• Nonequilibrium work energy relation for non-Hamiltonian dynamics
• Generalized integral fluctuation relation with feedback control for diffusion processes
• Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting
• Projection of strong coupling interaction with thermal bath in a polymer
• Entropy production due to spacetime fluctuations
• Equilibrium free energy differences at different temperatures from a single set of nonequilibrium transitions
• Work and heat exchanged during sudden quenches of strongly coupled quantum systems