Nonequilibrium microcanonical and canonical ensembles and their equivalence

Abstract

Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here we propose a theory of these ensembles that unifies and generalizes earlier results, and show how it is fundamentally related to the large deviation properties of nonequilibrium systems. Using this theory, we provide conditions for the equivalence of nonequilibrium ensembles, generalizing those found for equilibrium systems, construct driven physical processes that generate these ensembles, and re-derive in a simple way known and new product rules for their transition rates. A nonequilibrium diffusion model is used to illustrate these results.

v1: 5 pages, revtex, 1 figure; v2: minor corrections, some references added

References in corpus (9)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• 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
• The Einstein relation generalized to non-equilibrium
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Invariant quantities in shear flow
• Properties of a non-equilibrium heat bath
• Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models

Cited by in corpus (171)

• Nonequilibrium Markov processes conditioned on large deviations
• Universal bounds on current fluctuations
• Introduction to dynamical large deviations of Markov processes
• Unravelling the large deviation statistics of Markovian open quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Variational and optimal control representations of conditioned and driven processes
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Kinetic uncertainty relation
• Effective interactions and large deviations in stochastic processes
• Current large deviations for driven periodic diffusions
• Making rare events typical in Markovian open quantum systems
• Optimizing active work: Dynamical phase transitions, collective motion, and jamming
• A minimal model of dynamical phase transition
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Dynamical phase transition in drifted Brownian motion
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
• 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
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
• Diffusions conditioned on occupation measures
• Adaptive sampling of large deviations
• Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Fluctuating observation time ensembles in the thermodynamics of trajectories
• Large deviations at level 2.5 for Markovian open quantum systems: quantum jumps and quantum state diffusion
• Current fluctuations of interacting active Brownian particles
• Dynamical large deviations of reflected diffusions
• Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
• Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories
• Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics
• Universality in dynamical phase transitions of diffusive systems
• Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• The Airy distribution: experiment, large deviations and additional statistics
• Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics
• Condensation of Fluctuations in and out of Equilibrium
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Current fluctuations in boundary-driven quantum spin chains
• Extreme Quantum Advantage for Rare-Event Sampling
• Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process
• 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
• Microscopic Fluctuation Theory (mFT) for interacting Poisson processes
• Process interpretation of current entropic bounds
• Equivalence of matrix product ensembles of trajectories in open quantum systems
• Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom
• Large Deviations for the density and the current in Non-Equilibrium-Steady-States on disordered rings
• Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations
• Large deviations of random walks on random graphs
• Trajectory phase transitions in non-interacting spin systems
• Large deviations of currents in diffusions with reflective boundaries
• Intermittency and dynamical Lee-Yang zeros of open quantum systems
• Continuous information flow fluctuations
• Periodically driven jump processes conditioned on large deviations
• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Large deviations in the presence of cooperativity and slow dynamics
• Variational design principles for nonequilibrium colloidal assembly
• Role of current fluctuations in nonreversible samplers
• Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
• Non-intersecting Brownian bridges in the flat-to-flat geometry
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
• The grand canonical catastrophe as an instance of condensation of fluctuations
• Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs
• Large deviations and optimal control forces for hard particles in one dimension
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Work fluctuations of self-propelled particles in the phase separated state
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Thermodynamics of quantum trajectories on a quantum computer
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Catching and reversing quantum jumps and thermodynamics of quantum trajectories
• Jump-Drift and Jump-Diffusion Processes : Large Deviations for the density, the current and the jump-flow and for the excursions between jumps
• Nonequilibrium thermodynamic potentials for continuous-time Markov chains
• A large deviation theory perspective on nanoscale transport phenomena
• Entanglement statistics in Markovian open quantum systems: a matter of mutation and selection
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• Noise correction of large deviations with anomalous scaling
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Tricritical behavior in dynamical phase transitions
• A Deep Learning Functional Estimator of Optimal Dynamics for Sampling Large Deviations
• Long-range interactions, doubling measures and Tsallis entropy
• Graph-combinatorial approach for large deviations of Markov chains
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• Heterogeneity-induced large deviations in activity and (in some cases) entropy production
• Energy and Heat Fluctuations in a Temperature Quench
• Non equivalence of dynamical ensembles and emergent non ergodicity
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Occupation time statistics of a gas of interacting diffusing particles
• Thermodynamic formalism and linear response theory for non-equilibrium steady states
• Stochastic gene expression conditioned on large deviations
• Modeling of biomolecular machines in non-equilibrium steady states
• Living on the edge of instability
• Varied phenomenology of models displaying dynamical large-deviation singularities
• Extinctions of coupled populations, and rare-event dynamics under non-Gaussian noise
• Sampling rare fluctuations of discrete-time Markov chains
• BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts
• Universal Excursion and Bridge shapes in ABBM/CIR/Bessel processes
• Large deviations of the stochastic area for linear diffusions
• Entropy Regularized Reinforcement Learning Using Large Deviation Theory
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Conditioned random walks and interaction-driven condensation
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Absence of dissipation in trajectory ensembles biased by currents
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• Microcanonical conditioning of Markov processes on time-additive observables
• Localisation in space and time in disordered-lattice open quantum dynamics
• Biological implications of dynamical phases in non-equilibrium networks
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Microscopic biasing of discrete-time quantum trajectories
• Conditional reversibility in nonequilibrium stochastic systems
• Dynamical phase coexistence in the Fredrickson-Andersen model
• 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
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Macrostate equivalence of two general ensembles and specific relative entropies
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Adaptive power method for estimating large deviations in Markov chains
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium
• The explicit form of the rate function for semi-Markov processes and its contractions
• An introduction to large deviations with applications in physics
• Dynamical phase transitions in one-dimensional hard-particle systems
• 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
• Asymptotic equivalence of probability measures and stochastic processes
• Bringing together two paradigms of non-equilibrium: Fragile versus robust aging in driven glassy systems
• On correlations and fluctuations of time-averaged densities and currents with general time-dependence
• Meta-work and the analogous Jarzynski relation in ensembles of dynamical trajectories
• Thermodynamics of chaotic relaxation processes
• Long-ranged correlations in large deviations of local clustering
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Numerical comparison of a constrained path ensemble and a driven quasisteady state
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Maximal dispersion of adaptive random walks
• A unified perspective on exponential tilt and bridge algorithms for rare trajectories of discrete Markov processes
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• Dynamical equivalence classes for Markov jump processes
• Multi-point nonequilibrium umbrella sampling and associated fluctuation relations
• Poles, Shocks and Tygers: The Time-reversible Burgers equation
• Auxiliary open quantum system for the Floquet quantum master equation
• 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
• Breakdown of the Finite-Time and -Population Scalings of the Large Deviation Function in the Large-Size Limit of a Contact Process
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
• Understanding random-walk dynamical phase coexistence through waiting times
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Maximal Algorithmic Caliber and Algorithmic Causal Network Inference: General Principles of Real-World General Intelligence?
• Thermodynamic laws in isolated systems
• Fluctuation Relations associated to an arbitrary bijection in path space
• Conditioning two diffusion processes with respect to their first-encounter properties
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting
• Steering Active-Colloid Assembly by Biasing Dissipation
• Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Microcanonical ensemble out of equilibrium
• Making rare events typical in $d$-dimensional chaotic maps