Chaotic dynamics, fluctuations, nonequilibrium ensembles

DOI10.1063/1.166320zbMath0965.82011arXivchao-dyn/9712011OpenAlexW1965202306WikidataQ73463719 ScholiaQ73463719MaRDI QIDQ4515069

Giovanni Gallavotti

Publication date: 12 November 2000

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/chao-dyn/9712011

zbMATH Keywords

equilibrium statistical mechanicsfluctuation theoremergodic hypothesisnonequilibrium statistical mechanicschaotic hypothesis

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Foundations of time-dependent statistical mechanics (82C03) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Dynamical aspects of statistical mechanics (37A60)

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Cites Work

• The ergodic theory of axiom A flows
• SRB states and nonequilibrium statistical mechanics close to equilibrium
• Positivity of entropy production in nonequilibrium statistical mechanics
• Applications of periodic orbit theory to \(N\)-particle systems
• Differentiation of SRB states
• Reversibility, coarse graining and the chaoticity principle
• Chaotic principle: an experimental test.
• Equivalence of dynamical ensembles and Navier-Stokes equations.
• Probability of second law violations in shearing steady states
• Large deviation rule for Anosov flows
• Fluctuation theorem for stochastic dynamics
• Extension of Onsager's Reciprocity to Large Fields and the Chaotic Hypothesis