Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation

Abstract

Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics and associated structures. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.

41 pages, 10 figures

References in corpus (10)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• A numerical approach to large deviations in continuous-time
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Symmetries in Fluctuations Far from Equilibrium
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• 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
• Spontaneous symmetry breaking: variations on a theme

Cited by in corpus (74)

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• A minimal model of dynamical phase transition
• Fluctuations in ballistic transport from Euler hydrodynamics
• Dynamical phase transition in drifted Brownian motion
• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• Importance sampling large deviations in nonequilibrium steady states. I
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Convergence of large deviation estimators
• Building continuous time crystals from rare events
• Survival of a static target in a gas of diffusing particles with exclusion
• Exact symmetries in the velocity fluctuations of a hot Brownian swimmer
• Macroscopic Stochastic Thermodynamics
• Statistics of large currents in the Kipnis-Marchioro-Presutti model in a ring geometry
• Order and symmetry-breaking in the fluctuations of driven systems
• Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface
• Sampling rare events across dynamical phase transitions
• Current fluctuations in boundary-driven quantum spin chains
• Geometrical optics of constrained Brownian excursion: from the KPZ scaling to dynamical phase transitions
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Arrhenius law for interacting diffusive systems
• Role of current fluctuations in nonreversible samplers
• Isometric fluctuation relations for equilibrium states with broken symmetry
• Large deviations and optimal control forces for hard particles in one dimension
• Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
• Efficient characterisation of large deviations using population dynamics
• Weak additivity principle for current statistics in d-dimensions
• Observing symmetry-broken optimal paths of stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Large deviations in models of growing clusters with symmetry-breaking transitions
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting
• Large fluctuations in diffusion-controlled absorption
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter
• The kinetic exclusion process: a tale of two fields
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Occupation time statistics of a gas of interacting diffusing particles
• Spatial fluctuation theorem
• Isometric Uncertainty Relations
• Statistics of the dissipated energy in driven diffusive systems
• Dynamical phase coexistence in the Fredrickson-Andersen model
• Fluctuation relations for equilibrium states with broken discrete or continuous symmetries
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Rare event simulation for stochastic dynamics in continuous time
• Limit theorems for cloning algorithms
• Local structure of current fluctuations in diffusive systems beyond one dimension
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Probing local equilibrium in nonequilibrium fluids
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Scaling laws and bulk-boundary decoupling in heat flow
• Full absorption statistics of diffusing particles with exclusion
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Long-ranged correlations in large deviations of local clustering
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Current fluctuations in a stochastic system of classical particles with next-nearest-neighbor interactions
• Programmable time crystals from higher-order packing fields
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Emergence of particle clusters in a one-dimensional model: connection to condensation processes
• Critical behavior of a programmable time-crystal lattice gas
• Stochastic modeling of gene expression: application of ensembles of trajectories
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Fluctuation Relations associated to an arbitrary bijection in path space
• Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit
• Structure of the optimal path to a fluctuation
• Mechanical analysis of a dynamical phase transition for particles in a channel
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions