Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

Abstract

In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the observable, that we study through a biased dynamics in a large-deviation framework. We determine explicitly the effective probability-conserving dynamics which makes rare trajectories of the original dynamics become typical trajectories of the effective one. Our approach makes use of a weak-noise path-integral description in which the action is minimised by the rare trajectories of interest. For `current-type' additive observables, we find the emergence of a propagative trajectory minimising the action for large enough deviations, revealing the existence of a dynamical phase transition at a fluctuating level. In addition, we provide a new method to determine the scaled cumulant generating function of the observable without having to optimise the action. It allows one to show that the weak-noise and the large-time limits commute in this problem. Finally, we show how the biased dynamics can be mapped in practice to an effective driven dynamics, which takes the form of a driven Langevin dynamics in an effective potential. The non-trivial shape of this effective potential is key to understand the link between the dynamical phase transition in the large deviations of current and the standard depinning transition of a particle in a tilted potential.

References in corpus (51)

• The large deviation approach to statistical mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Thermodynamic formalism for systems with Markov dynamics
• Direct evaluation of large-deviation functions
• Nonequilibrium Markov processes conditioned on large deviations
• Thermodynamics of Quantum Jump Trajectories
• Macroscopic current fluctuations in stochastic lattice gases
• Large deviations and ensembles of trajectories in stochastic models
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Simulating rare events in dynamical processes
• Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves
• Introduction to dynamical large deviations of Markov processes
• Non equilibrium current fluctuations in stochastic lattice gases
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Cumulants and large deviations of the current through non-equilibrium steady states
• Population dynamics method with a multi-canonical feedback control
• Effective interactions and large deviations in stochastic processes
• Chaotic properties of systems with Markov dynamics
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Rules for transition rates in nonequilibrium steady states
• Observable and hidden singular features of large fluctuations in nonequilibrium systems
• Current large deviations for driven periodic diffusions
• Making rare events typical in Markovian open quantum systems
• A minimal model of dynamical phase transition
• Distribution of Entropy Production for a Colloidal Particle in a Nonequilibrium Steady State
• Go with the Winners: a General Monte Carlo Strategy
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Large deviation function for entropy production in driven one-dimensional systems
• Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux
• Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
• Microscopic structure of shocks and antishocks in the ASEP conditioned on low current
• Lagrangian phase transitions in nonequilibrium thermodynamic systems
• Phase transitions in large deviations of reset processes
• Adaptive sampling of large deviations
• Large deviation function for the entropy production: Optimal trajectory and role of fluctuations
• Invariant quantities in shear flow
• Activity phase transition for constrained dynamics
• Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems
• Lower current large deviations for zero-range processes on a ring

Cited by in corpus (47)

• Large deviations and dynamical phase transitions in stochastic chemical networks
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
• Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Large-deviation theory for a Brownian particle on a ring: a WKB approach
• Dynamical large deviations of linear diffusions
• Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
• Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
• Trajectory phase transitions in non-interacting spin systems
• Nonequilibirum steady state for harmonically-confined active particles
• Optimal sampling of dynamical large deviations via matrix product states
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Jump-Drift and Jump-Diffusion Processes : Large Deviations for the density, the current and the jump-flow and for the excursions between jumps
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• Efficiency of one-dimensional active transport conditioned on motility
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• Thermodynamic Control of Activity Patterns in Cytoskeletal Networks
• Living on the edge of instability
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Microcanonical conditioning of Markov processes on time-additive observables
• Symmetry-induced fluctuation relations in open quantum systems
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Markov trajectories : Microcanonical Ensembles based on empirical observables as compared to Canonical Ensembles based on Markov generators
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• Conditioning diffusion processes with respect to the local time at the origin
• A giant disparity and a dynamical phase transition in large deviations of the time-averaged size of stochastic populations
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Conditioning two diffusion processes with respect to their first-encounter properties
• Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions