Fluctuation relations for anomalous dynamics

Abstract

We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the probability distributions of mechanical and thermodynamical work in two paradigmatic nonequilibrium situations, respectively: a particle subject to a constant force and a particle in a harmonic potential dragged by a constant force. We check the transient FR for two models exhibiting superdiffusion, where a fluctuation-dissipation relation does not exist, and for two other models displaying subdiffusion, where there is a fluctuation-dissipation relation. In the two former cases the conventional transient FR is not recovered, whereas in the latter two it holds either exactly or in the long-time limit.

Letter, 9 pages, no figures

References in corpus (19)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Steady State Thermodynamics of Langevin Systems
• The Nonequilibrium Thermodynamics of Small Systems
• Fluctuation theorems for stochastic dynamics
• Anomalous dynamics of cell migration
• Langevin equations for continuous time Lévy flights
• Work fluctuation theorems for harmonic oscillators
• Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
• Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
• Anomalous Diffusion of Inertial, Weakly Damped Particles
• Joint Probability Distributions for a Class of Non-Markovian Processes
• Non-equilibrium work fluctuations for oscillators in non-Markovian baths
• Continuous time random walk for open systems: Fluctuation theorems and counting statistics
• Superstatistical generalization of the work fluctuation theorem
• Fluctuation relation for a Lévy particle
• Nonequilibrium steady state thermodynamics and fluctuations for stochastic systems

Cited by in corpus (30)

• Steady state fluctuation relations for systems driven by an external random force
• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
• Current fluctuations in stochastic systems with long-range memory
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• Anomalous fluctuation relations
• On the stochastic thermodynamics of fractional Brownian motion
• Feynman-Kac equation for anomalous processes with space- and time-dependent forces
• On anomalous diffusion and the out of equilibrium response function in one-dimensional models
• Anomalous dynamical scaling determines universal critical singularities
• Normal and Anomalous Fluctuation Relations for Gaussian Stochastic Dynamics
• Fluctuation relations without uniform large deviations
• Fluctuation relation and heterogeneous superdiffusion in glassy transport
• Non-adiabatic entropy production for non-Markov dynamics
• Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
• Fluctuations in interacting particle systems with memory
• Underdamped stochastic harmonic oscillator
• Heat and work distributions for mixed Gauss-Cauchy process
• A generalized fluctuation relation for power-law distributions
• Steady state fluctuation relation and time-reversibility for non-smooth chaotic maps
• Lévy flights and Lévy walks under stochastic resetting
• Transient photocurrent and optical absorption of disordered thin-film semiconductors: in-depth injection and nonlinear response
• Microreversibility and driven Brownian motion with hydrodynamic long-time correlations
• Stochastic thermodynamics of a tagged particle within a harmonic chain
• Statistical Dynamics of Regional Populations and Economies
• Underdamped, anomalous kinetics in double-well potentials
• Yielding and large deviations in micellar gels: a model
• Fluctuation relation in continuous-time random walks driven by an external field
• Generalized Fokker-Planck equation and its solution for linear non-Markovian Gaussian systems
• Duration of local violations of the second law of thermodynamics along single trajectories in phase space
• Symmetry for the duration of entropy-consuming intervals