Effective interactions and large deviations in stochastic processes

Abstract

We discuss the relationships between large deviations in stochastic systems, and "effective interactions" that induce particular rare events. We focus on the nature of these effective interactions in physical systems with many interacting degrees of freedom, which we illustrate by reviewing several recent studies. We describe the connections between effective interactions, large deviations at "level 2.5", and the theory of optimal control. Finally, we discuss possible physical applications of variational results associated with those theories.

12 pages

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Cited by in corpus (92)

• Unravelling the large deviation statistics of Markovian open quantum systems
• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• Variational and optimal control representations of conditioned and driven processes
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Population dynamics method with a multi-canonical feedback control
• Current large deviations for driven periodic diffusions
• Optimizing active work: Dynamical phase transitions, collective motion, and jamming
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Phase separation and large deviations of lattice active matter
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
• Conformal invariance in driven diffusive systems at high currents
• Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
• A reinforcement learning approach to rare trajectory sampling
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Collective motion in large deviations of active particles
• Dynamical large deviations of reflected diffusions
• Canonical structure and orthogonality of forces and currents in irreversible Markov chains
• Learning nonequilibrium control forces to characterize dynamical phase transitions
• Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations
• Reinforcement learning of rare diffusive dynamics
• Perspective: How to overcome dynamical density functional theory
• Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
• Dynamical large deviations of linear diffusions
• Process interpretation of current entropic bounds
• Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
• Periodically driven jump processes conditioned on large deviations
• Giant leaps and long excursions: fluctuation mechanisms in systems with long-range memory
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
• Role of current fluctuations in nonreversible samplers
• Importance sampling in path space for diffusion processes with slow-fast variables
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Large deviations and optimal control forces for hard particles in one dimension
• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases
• Variance of fluctuations from Noether invariance
• 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
• Catching and reversing quantum jumps and thermodynamics of quantum trajectories
• Large deviations in models of growing clusters with symmetry-breaking transitions
• A large deviation theory perspective on nanoscale transport phenomena
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• 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
• Extreme events in stochastic transport on networks
• Tricritical behavior in dynamical phase transitions
• 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
• Stochastic gene expression conditioned on large deviations
• Biased ensembles of pulsating active matter
• Sampling rare fluctuations of discrete-time Markov chains
• Absence of dissipation in trajectory ensembles biased by currents
• Microcanonical conditioning of Markov processes on time-additive observables
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Dynamical phase coexistence in the Fredrickson-Andersen model
• On Effective Stochastic Generators for Conditioned Dynamics at an Atypical Reaction-Diffusion Current
• 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
• Finding the effective dynamics to make rare events typical in chaotic maps
• An introduction to large deviations with applications in physics
• 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
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• Bringing together two paradigms of non-equilibrium: Fragile versus robust aging in driven glassy systems
• Conditioning diffusion processes with respect to the local time at the origin
• Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics
• 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
• Multi-point nonequilibrium umbrella sampling and associated fluctuation relations
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Current fluctuations in a stochastic system of classical particles with next-nearest-neighbor interactions
• Markov generators as non-hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and Singular Value Decompositions
• 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 ?
• Effective dynamics in an asymmetric death-branching process
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Enantiodromic effective generators of a Markov jump process with Gallavotti-Cohen symmetry
• Non-empirical weighted Langevin mechanics for the potential escape problem: parallel algorithm and application to the Argon clusters
• Effective bandwidth of non-Markovian packet traffic
• Stochastic modeling of gene expression: application of ensembles of trajectories
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Non-equilibrium pathways between cluster morphologies in active phase separation: necking, rupture and cavitation
• Conditioning two diffusion processes with respect to their first-encounter properties
• Localization properties of the sparse Barrat-Mézard trap model
• Fluctuation Relations associated to an arbitrary bijection in path space