Conceptual and practical approaches for investigating irreversible processes

Abstract

Current research in statistical mechanics mostly concerns the investigation of out-of-equilibrium, irreversible processes, which are ubiquitous in nature and still far from being theoretically understood. Even the precise characterization of irreversibility is the object of an open debate: while in the context of Hamiltonian systems the one-century-old proposal by M. Smoluchowski looks still valid (a process appears irreversible when the initial state has a recurrence time that is long compared to the time of observation [1]), in dissipative systems, particularly in the case of stochastic processes, the problem is more involved, and quantifying the "degree of irreversibility" is a pragmatic need. The most employed strategies rely on the estimation of entropy production: this quantity, although mathematically well-defined, is often difficult to compute, especially when analyzing experimental data. Moreover, being a global observable, entropy production fails to capture specific aspects of irreversibility in extended systems, such as the role of different currents and their spatial development. This review aims to address various conceptual and technical challenges encountered in the analysis of irreversibility, including the role of the coarse-graining procedure and the treatment of data in the absence of complete information. The discussion will be mostly based on simple models, analytically treatable, and supplemented by examples of complex, more realistic non-equilibrium systems.

79 pages, 19 figures

References in corpus (40)

• Thermodynamic uncertainty relation for biomolecular processes
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Fluctuations and response of nonequilibrium states
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Lower bounds on dissipation upon coarse graining
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Experimental Realization of a Minimal Microscopic Heat Engine
• Brownian motors in micro-scale domain: Enhancement of efficiency by noise
• Entropy production and coarse-graining in Markov processes
• Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise
• Variance Sum Rule for Entropy Production
• The fluctuation-dissipation relation: how does one compare correlation functions and responses?
• Cages and anomalous diffusion in vibrated dense granular media
• Direct Route to Thermodynamic Uncertainty Relations and Their Saturation
• Entropy production of Multivariate Ornstein-Uhlenbeck processes correlates with consciousness levels in the human brain
• Classical pendulum clocks break the thermodynamic uncertainty relation
• Time-resolved statistics of snippets as general framework for model-free entropy estimators
• Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls
• On the thermal equilibrium state of large scale flows
• Turbulence: does energy cascade exist?
• Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence
• Information-theoretic analysis of the directional influence between cellular processes
• Thermodynamic Uncertainty Relation in Interacting Many-Body Systems
• Thermodynamic bounds for diffusion in non-equilibrium systems with multiple timescales
• Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior
• Ergodic observables in non-ergodic systems: the example of the harmonic chain
• Mechanism for giant enhancement of transport induced by active fluctuations
• Extracting causation from millennial-scale climate fluctuations in the last 800 kyr
• A data-driven framework for dimensionality reduction and causal inference in climate fields
• Response and flux of information in extended non-equilibrium dynamics
• Time irreversibility and multifractality of power along single particle trajectories in turbulence
• Discrete synaptic events induce global oscillations in balanced neural networks
• Irreversibility and typicality: A simple analytical result for the Ehrenfest model
• Statistical features of systems driven by non-Gaussian processes: theory & practice
• Thermodynamic uncertainty relations in the presence of non-linear friction and memory
• Thermodynamic precision of a chain of motors: the difference between phase and noise correlation
• Non-equilibrium statistical mechanics of the turbulent energy cascade: irreversibility and response functions
• A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics
• Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics

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• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Force-free kinetic inference of entropy production
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• Unravelling the Flow of Information in a Nonequilibrium Process in the Presence of Hydrodynamic Interactions