Large deviation approach to nonequilibrium systems

Abstract

The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A similar approach has been followed more recently for nonequilibrium systems, especially in the context of interacting particle systems. We review here the basis of this approach, emphasizing the similarities and differences that exist between the application of large deviation theory for studying equilibrium systems on the one hand and nonequilibrium systems on the other. Of particular importance are the notions of macroscopic, hydrodynamic, and long-time limits, which are analogues of the equilibrium thermodynamic limit, and the notion of statistical ensembles which can be generalized to nonequilibrium systems. For the purpose of illustrating our discussion, we focus on applications to Markov processes, in particular to simple random walks.

26 pages, draft book chapter [Klages, Rainer / Just, Wolfram / Jarzynski, Christopher (eds.), Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond, 2013. Approx 350 pages with approx 100 figures. Hardcover. ISBN: 978-3-527-41094-1 (WILEY-VCH, Weinheim) http://www.wiley.com]. v2: Minor corrections

References in corpus (15)

• The large deviation approach to statistical mechanics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Steady state statistics of driven diffusions
• Symmetries in Fluctuations Far from Equilibrium
• Current large deviation function for the open asymmetric simple exclusion process
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Large Fluctuations in Driven Dissipative Media
• Current fluctuations in stochastic systems with long-range memory
• Minimum entropy production principle from a dynamical fluctuation law
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Reflection positivity and phase transitions in lattice spin models
• A selection of nonequilibrium issues

Cited by in corpus (44)

• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
• Introduction to dynamical large deviations of Markov processes
• Variational and optimal control representations of conditioned and driven processes
• Large deviations for Markov processes with resetting
• On Bayesian Mechanics: A Physics of and by Beliefs
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Fluctuations in ballistic transport from Euler hydrodynamics
• Transport fluctuations in integrable models out of equilibrium
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Anomalous scaling of dynamical large deviations
• Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines
• Phase transitions in large deviations of reset processes
• Large deviations of the maximum of independent and identically distributed random variables
• Microscopic Fluctuation Theory (mFT) for interacting Poisson processes
• Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
• 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
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Emergent second law for non-equilibrium steady states
• Heat exchanges in a quenched ferromagnet
• Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Real-Space Renormalization for disordered systems at the level of Large Deviations
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Singularities in Large Deviation Functionals of Bulk-Driven Transport Models
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• Inverse Design of Non-Equilibrium Steady-States: A Large Deviation Approach
• 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
• Regarding Flows Under the Free Energy Principle: A Comment on "How Particular is the Physics of the Free Energy Principle?" by Aguilera, Millidge, Tschantz, and Buckley
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Full Current Statistics for a Disordered Open Exclusion Process
• Markov generators as non-hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and Singular Value Decompositions
• Large Deviations of Irreversible Processes
• Path-reversal, Doi-Peliti generating functionals, and dualities between dynamics and inference for stochastic processes
• Effective bandwidth of non-Markovian packet traffic
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Coarse-graining nonequilibrium diffusions with Markov chains
• Asymmetric scaling in large deviations for rare values bigger or smaller than the typical value