Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

Abstract

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or non-equilibrium steady states on all time scales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all time scales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.

arXiv commentVersion accepted for publication in Physical Review Letters

References in corpus (74)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Thermodynamic uncertainty relation for biomolecular processes
• Steady State Thermodynamics of Langevin Systems
• Dissipation bounds all steady-state current fluctuations
• Macroscopic fluctuation theory
• How far from equilibrium is active matter?
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Single-molecule experiments in biological physics: methods and applications
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Stochastic Ergodicity Breaking: a Random Walk Approach
• Broken detailed balance and non-equilibrium dynamics in living systems
• Macroscopic current fluctuations in stochastic lattice gases
• Universal bounds on current fluctuations
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Estimating dissipation from single stationary trajectories
• Fluctuation theorem for currents and Schnakenberg network theory
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Quantifying dissipation using fluctuating currents
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
• Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells
• Current fluctuations and transport efficiency for general Langevin systems
• Introduction to dynamical large deviations of Markov processes
• Stochastic Path Integral Formulation of Full Counting Statistics
• Generic Properties of Stochastic Entropy Production
• Thermodynamic uncertainty relation for time-dependent driving
• Inferring entropy production from short experiments
• Inferring dissipation from current fluctuations
• Dissipation and lag in irreversible processes
• Unified thermodynamic uncertainty relations in linear response
• Multidimensional thermodynamic uncertainty relations
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Estimating entropy production by machine learning of short-time fluctuating currents
• Steady state statistics of driven diffusions
• The Local and the Occupation Time of a Particle Diffusing in a Random Medium
• Stochastic thermodynamics: From principles to the cost of precision
• A formal view on 2.5 large deviations and fluctuation relations
• Bounds on current fluctuations in periodically driven systems
• Fluctuation-Dissipation theorems and entropy production in relaxational systems
• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• Inferring the dynamics of underdamped stochastic systems
• Broken Detailed Balance of Filament Dynamics in Active Networks
• Frenetic bounds on the entropy production
• Learning force fields from stochastic trajectories
• Improving thermodynamic bounds using correlations
• A fractional Feynman-Kac equation for weak ergodicity breaking
• Emergent memory and kinetic hysteresis in strongly driven networks
• From Non-normalizable Boltzmann-Gibbs statistics to infinite-ergodic theory
• Level 2 large deviation functionals for systems with and without detailed balance
• A Decomposition of Irreversible Diffusion Processes Without Detailed Balance
• Information-theoretical bound of the irreversibility in thermal relaxation processes
• Irreversible local Markov chains with rapid convergence towards equilibrium
• Physically consistent numerical solver for time-dependent Fokker-Planck equations
• Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems
• Irreversibility in dynamical phases and transitions
• Computation of current cumulants for small nonequilibrium systems
• Canonical structure and orthogonality of forces and currents in irreversible Markov chains
• Monotone return to steady nonequilibrium
• Building general Langevin models from discrete data sets
• Large deviations of currents in diffusions with reflective boundaries
• On the relaxation to nonequilibrium steady states
• Non-Equilibrium Thermodynamics and Topology of Currents
• Unfolding Tagged Particle Histories in Single-File Diffusion: Exact Single- and Two-Tag Local Times Beyond Large Deviation Theory
• Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
• Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
• A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates
• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media
• Possible extended forms of thermodynamic entropy
• Optimal inference strategies and their implications for the linear noise approximation
• Deterministic model of battery, uphill currents and non-equilibrium phase transitions
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal

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• Variance Sum Rule for Entropy Production
• Direct Route to Thermodynamic Uncertainty Relations and Their Saturation
• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
• General theory for localizing the where and when of entropy production meets single-molecule experiments
• Perspective: Time irreversibility in systems observed at coarse resolution
• Model-free inference of memory in conformational dynamics of a multi-domain protein
• Effective estimation of entropy production with lacking data
• Thermodynamic bounds on generalized transport: From single-molecule to bulk observables
• On the emergence of memory in equilibrium versus non-equilibrium systems
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Variance sum rule: proofs and solvable models
• The Dance of Odd-Diffusive Particles: A Fourier Approach
• On correlations and fluctuations of time-averaged densities and currents with general time-dependence
• Precisely controlled colloids: A playground for path-wise non-equilibrium physics
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• Force-free kinetic inference of entropy production