Large deviation function for the entropy production: Optimal trajectory and role of fluctuations

Abstract

We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches: the Donsker-Varadhan theory and the Freidlin-Wentzell theory. We show that the wings of the large deviation function are dominated by a single optimal trajectory: either in forward (positive rate) or in backward direction (negative rate). The joining of both branches at zero entropy production implies a non-differentiability and thus the appearance of a "kink". However, around zero entropy production many trajectories contribute and thus the kink is smeared out.

References in corpus (26)

• The large deviation approach to statistical mechanics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Thermodynamic formalism for systems with Markov dynamics
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
• The Einstein relation generalized to non-equilibrium
• Entropy production and time asymmetry in nonequilibrium fluctuations
• Work fluctuation theorems for harmonic oscillators
• Functional determinants by contour integration methods
• Distribution of Entropy Production for a Colloidal Particle in a Nonequilibrium Steady State
• Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
• Fluctuation theorem and large deviation function for a solvable model of a molecular motor
• Surmounting Oscillating Barriers: Path-integral approach for Weak Noise
• Large deviation function for entropy production in driven one-dimensional systems
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Experimental Accessibility of Generalized Fluctuation-Dissipation Relations for Nonequilibrium Steady States
• Fluctuation Theorem for the flashing ratchet model of molecular motors
• Finite size scaling of current fluctuations in the totally asymmetric exclusion process
• Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models
• Entropy production in the non-equilibrium steady states of interacting many-body systems
• Entropy production in nonequilibrium steady states: A different approach and an exactly solvable canonical model
• Fluctuation relations with intermittent non-Gaussian variables
• Work probability distribution and tossing a biased coin

Cited by in corpus (38)

• Universal bounds on current fluctuations
• Numerical computation of rare events via large deviation theory
• Current large deviations for driven periodic diffusions
• A minimal model of dynamical phase transition
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• Dynamic phase transitions in simple driven kinetic networks
• Level 2 large deviation functionals for systems with and without detailed balance
• Large Deviation Function for a Driven Underdamped Particle in a Periodic Potential
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
• Large-deviation theory for a Brownian particle on a ring: a WKB approach
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Current fluctuations in periodically driven systems
• Current fluctuations of interacting active Brownian particles
• Macroscopic Stochastic Thermodynamics
• Learning nonequilibrium control forces to characterize dynamical phase transitions
• Trajectory phase transitions in non-interacting spin systems
• Large deviations in the presence of cooperativity and slow dynamics
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Evolutionary reinforcement learning of dynamical large deviations
• Fine-structured large deviations and the fluctuation theorem: Molecular motors and beyond
• Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• Efficiency fluctuations in cyclic machines
• Probability distributions with singularities
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Large deviations of a long-time average in the Ehrenfest Urn Model
• Entropy production and large deviation function for systems with microscopically irreversible transitions
• Statistical fluctuations under resetting: rigorous results
• Optimizing thermodynamic trajectories using evolutionary and gradient-based reinforcement learning
• Current fluctuations of a self-interacting diffusion on a ring
• Multi-point nonequilibrium umbrella sampling and associated fluctuation relations
• Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• Large deviation statistics of non-equilibrium fluctuations in a sheared model-fluid
• Work fluctuations for a confined Brownian particle: the role of initial conditions
• Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion
• Steering Active-Colloid Assembly by Biasing Dissipation
• Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit