Direct evaluation of dynamical large-deviation rate functions using a variational ansatz

Abstract

We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a time-extensive dynamical observable. We construct a reference model, a variational ansatz for the behavior of the original model conditioned on atypical values of the observable. Direct simulation of the reference model provides an upper bound on the large-deviation rate function associated with the original model, an estimate of the tightness of the bound, and, if the ansatz is chosen well, the exact rate function. The exact rare behavior of the original model does not need to be known in advance. We use this method to calculate rate functions for currents and counting observables in a set of network- and lattice models taken from the literature. Straightforward ansatze yield bounds that are tighter than bounds obtained from Level 2.5 of large deviations via approximations that involve uniform scalings of rates. We show how to correct these bounds in order to recover the rate functions exactly. Our approach is complementary to more specialized methods, and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations.

References in corpus (52)

• 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 large deviation approach to statistical mechanics
• 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
• Fluctuation theorem for stochastic dynamics
• Dissipation bounds all steady-state current fluctuations
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• The Fluctuation Theorem as a Gibbs Property
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Direct evaluation of large-deviation functions
• Universal bounds on current fluctuations
• Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
• Nonequilibrium glassy dynamics of self-propelled hard disks
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• A numerical approach to large deviations in continuous-time
• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Variational and optimal control representations of conditioned and driven processes
• Activity driven fluctuations in living cells
• Effective interactions and large deviations in stochastic processes
• Current large deviations for driven periodic diffusions
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics
• Biochemical machines for the interconversion of mutual information and work
• Anomalous scaling of dynamical large deviations
• Rare behavior of growth processes via umbrella sampling of trajectories
• Dynamic phase transitions in simple driven kinetic networks
• Importance sampling large deviations in nonequilibrium steady states. I
• Adaptive sampling of large deviations
• Allocating dissipation across a molecular machine cycle to maximize flux
• Convergence of large deviation estimators
• Large deviation function for the entropy production: Optimal trajectory and role of fluctuations
• Fluctuating observation time ensembles in the thermodynamics of trajectories
• Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
• Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories
• Current fluctuations in systems with diffusive dynamics, in and out of equilibrium
• Fluctuations of power injection in randomly driven granular gases
• Large Deviations in Fast-Slow Systems
• Large deviations in the presence of cooperativity and slow dynamics
• Fluctuations in interacting particle systems with memory
• Application of importance sampling to the computation of large deviations in non-equilibrium processes
• Sampling rare fluctuations of discrete-time Markov chains
• Trajectory reweighting for non-equilibrium steady states
• Multi-point nonequilibrium umbrella sampling and associated fluctuation relations

Cited by in corpus (21)

• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• Ergodicity and large deviations in physical systems with stochastic dynamics
• A reinforcement learning approach to rare trajectory sampling
• Collective motion in large deviations of active particles
• Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations
• Trajectory phase transitions in non-interacting spin systems
• Finite time large deviations via matrix product states
• Direct evaluation of rare events in active matter from variational path sampling
• Evolutionary reinforcement learning of dynamical large deviations
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Large deviations and optimal control forces for hard particles in one dimension
• A large deviation theory perspective on nanoscale transport phenomena
• Efficiency of one-dimensional active transport conditioned on motility
• A Deep Learning Functional Estimator of Optimal Dynamics for Sampling Large Deviations
• Variational deep learning of equilibrium transition path ensembles
• Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
• Thermodynamic uncertainty relation for Langevin dynamics by scaling time
• Varied phenomenology of models displaying dynamical large-deviation singularities
• Efficient large deviation estimation based on importance sampling
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory