On the stochastic thermodynamics of fractional Brownian motion
arXiv:2205.15791 · doi:10.1103/PhysRevResearch.4.043186
Abstract
This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus, there is no conventional fluctuation-dissipation relation (FDR) of the second kind and no unique way to define a temperature. We start from a Markovian process with time-dependent diffusivity (an example being scaled Brownian motion). It turns out that standard stochastic thermodynamic notions can be applied rather straightforwardly by introducing a time-dependent temperature, yielding the integral fluctuation relation. We then proceed to our focal system, that is, a particle undergoing fractional Brownian motion (FBM). In this system, the noise is Gaussian but the noise correlation function is nonlocal in time, defining a non- Markovian process. We analyse in detail the consequences when using the conventional notions of stochastic thermodynamics with a constant medium temperature. In particular, the heat calculated from dissipation into the medium differs from the log ratio of path probabilities of forward and backward motion, yielding a deviation from the standard integral fluctuation relation for the total entropy production if the latter is defined via system entropy and heat exchange. These apparent inconsistencies can be circumvented by formally defining a time-nonlocal temperature that fulfils a generalized FDR. To shed light on the rather abstract quantities resulting from the latter approach we perform a perturbation expansion. This allows us to calculate analytically, up to linear order, the generalized temperature and the corresponding heat exchange. By this, we provide explicit expressions and a physical interpretation for the leading corrections induced by non-Markovianity.
References in corpus (75)
- A nonequilibrium equality for free energy differences
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- The Mechanics and Statistics of Active Matter
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Entropy production along a stochastic trajectory and an integral fluctuation theorem
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
- Anomalous transport in the crowded world of biological cells
- Fluctuation theorem for stochastic dynamics
- Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
- Thermodynamic uncertainty relation for biomolecular processes
- Information heat engine: converting information to energy by feedback control
- Path ensembles averages in systems driven far-from-equilibrium
- In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
- The Nonequilibrium Thermodynamics of Small Systems
- Stochastic thermodynamics: Principles and perspectives
- Stochastic thermodynamics under coarse-graining
- Single-molecule experiments in biological physics: methods and applications
- Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
- Anomalous dynamics of cell migration
- The effective temperature
- Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
- Irreversibility in active matter systems: Fluctuation theorem and mutual information
- Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
- A fluctuation theorem for currents and non-linear response coefficients
- Entropy production of active particles and for particles in active baths
- Irreversibility, heat and information flows induced by non-reciprocal interactions
- Anomalous thermodynamics at the micro-scale
- Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
- Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
- Thermodynamic uncertainty relation for general open quantum systems
- Loopy Lévy flights enhance tracer diffusion in active suspensions
- Non-equilibrium work fluctuations for oscillators in non-Markovian baths
- Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
- Active Brownian Heat Engines
- Generalized arcsine laws for fractional Brownian motion
- Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields
- Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control
- Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
- An operational approach to quantum stochastic thermodynamics
- Continuous time random walk for open systems: Fluctuation theorems and counting statistics
- Effects of active fluctuations on energetics of a colloidal particle: superdiffusion, dissipation and entropy production
- Entropy production and work fluctuation relations for a single particle in active bath
- Superstatistical generalization of the work fluctuation theorem
- Clausius relation for active particles: what can we learn from fluctuations?
- Classical pendulum clocks break the thermodynamic uncertainty relation
- Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries
- Effective temperatures of hot Brownian motion
- Heat flow due to time-delayed feedback
- Fluctuation relations for anomalous dynamics
- Fluctuation relation for a Lévy particle
- Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
- Friction and noise for a probe in a nonequilibrium fluid
- Fluctuation properties of an effective nonlinear system subject to Poisson noise
- Perturbative Expansion for the Maximum of Fractional Brownian Motion
- Anomalous fluctuation relations
- Path Integral Formulation for Lévy Flights - Evaluation of the Propagator for Free, Linear and Harmonic Potentials in the Over- and Underdamped Limits
- Stochastic thermodynamics of self-oscillations: the electron shuttle
- Experimental Evidence of Fluctuation-Dissipation Theorem Violation in a Superspin Glass
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations
- First passage in an interval for fractional Brownian motion
- Thermodynamic uncertainty relation for time-delayed Langevin systems
- Uncertainty relations for time-delayed Langevin systems
- Molecular theory of anomalous diffusion
- Generalized fluctuation relation and effective temperatures in a driven fluid
- Normal and Anomalous Fluctuation Relations for Gaussian Stochastic Dynamics
- Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
- Fluctuation relation and heterogeneous superdiffusion in glassy transport
- A generalized fluctuation relation for power-law distributions
- Heat and work distributions for mixed Gauss-Cauchy process
- A fluctuation relation for weakly ergodic aging systems
- Search efficiency of discrete fractional Brownian motion in a random distribution of targets
- Non-Clausius heat transfer: The method of the nonstationary Langevin equation
- Work relations for a system governed by Tsallis statistics