Symmetries in Fluctuations Far from Equilibrium

Abstract

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.

8 pages, 4 figures

References in corpus (23)

• The large deviation approach to statistical mechanics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Thermal conduction in classical low-dimensional lattices
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Heat Transport in low-dimensional systems
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Fluctuations in Stationary non Equilibrium States
• Direct evaluation of large-deviation functions
• Macroscopic current fluctuations in stochastic lattice gases
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Stochastic interacting particle systems out of equilibrium
• A fluctuation theorem for currents and non-linear response coefficients
• A simple one-dimensional model of heat conduction which obeys Fourier's law
• Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Breakdown of Hydrodynamics in a Simple One-Dimensional Fluid
• Boundary Dissipation in a Driven Hard Disk System
• On the long range correlations of thermodynamic systems out of equilibrium
• Nonequilibrium fluctuations in small systems: From physics to biology

Cited by in corpus (78)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Macroscopic fluctuation theory
• Hot Brownian Motion
• Simulating rare events in dynamical processes
• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Spontaneous Symmetry Breaking at the Fluctuating Level
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• Nonequilibrium potential and fluctuation theorems for quantum maps
• Nonequilibrium and irreversibility
• Dynamical phase transition for current statistics in a simple driven diffusive system
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
• Large fluctuations and dynamic phase transition in a system of self-propelled particles
• Symmetry and the thermodynamics of currents in open quantum systems
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Large deviation approach to nonequilibrium systems
• Harnessing symmetry to control quantum transport
• Hot Microswimmers
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• Large Fluctuations in Driven Dissipative Media
• Exact symmetries in the velocity fluctuations of a hot Brownian swimmer
• Nonlinear driven diffusive systems with dissipation: fluctuating hydrodynamics
• Order and symmetry-breaking in the fluctuations of driven systems
• Joint probability distributions and fluctuation theorems
• Extreme fluctuations of active Brownian motion
• Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation
• Universal anomalous fluctuations in charged single-file systems
• Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Correlations of the density and of the current in non-equilibrium diffusive systems
• Entropy production and its large deviations in an active lattice gas
• Large deviations in boundary-driven systems: Numerical evaluation and effective large-scale behavior
• Isometric fluctuation relations for equilibrium states with broken symmetry
• Infinite family of second-law-like inequalities
• Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
• Fluctuation relations for anisotropic systems
• Variance of fluctuations from Noether invariance
• Weak additivity principle for current statistics in d-dimensions
• Microreversibility, nonequilibrium current fluctuations, and response theory
• Microreversibility, fluctuations, and nonlinear transport in transistors
• Large deviations in the symmetric simple exclusion process with slow boundaries
• The kinetic exclusion process: a tale of two fields
• Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter
• Compact Waves in Microscopic Nonlinear Diffusion
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Counting statistics and microreversibility in stochastic models of transistors
• Stochastic approach and fluctuation theorem for charge transport in diodes
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Spatial fluctuation theorem
• Statistics of the dissipated energy in driven diffusive systems
• Isometric Uncertainty Relations
• Density large deviations for multidimensional stochastic hyperbolic conservation laws
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Fluctuation relations for equilibrium states with broken discrete or continuous symmetries
• Spectral signatures of symmetry-breaking dynamical phase transitions
• A topological fluctuation theorem
• Symmetry-induced fluctuation relations in open quantum systems
• Random paths and current fluctuations in nonequilibrium statistical mechanics
• Microreversibility and nonequilibrium response theory in magnetic fields
• Probing local equilibrium in nonequilibrium fluids
• Local structure of current fluctuations in diffusive systems beyond one dimension
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Scaling laws and bulk-boundary decoupling in heat flow
• Microreversibility and quantum transport in Aharonov-Bohm rings
• Current loops and fluctuations in the zero-range process on a diamond lattice
• Microreversibility, nonequilibrium response, and Euler's polynomials
• Macroscopic fluxes and local reciprocal relation in second-order stochastic processes far from equilibrium
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Generalized fluctuation theorems for classical systems
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Properties of the dissipation functions for passive and active systems
• The mathematical law of evolutionary information dynamics and an observer's evolution regularities
• Fluctuation Relations associated to an arbitrary bijection in path space
• Structure of the optimal path to a fluctuation