The Fluctuation Theorem as a Gibbs Property

1998/12/18 by Christian Maes · 482 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Computer science #Dynamical systems theory #Fluctuation theorem #Formalism (music) #Gibbs measure #Gibbs state #H-theorem #Mathematics #Maximum entropy thermodynamics #Measure (data warehouse) #Non-equilibrium thermodynamics #Physics #Pure mathematics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Symbolic dynamics #math-ph #math.DS #math.MP #msc:60F10 #msc:82C05

paper · pdf · doi:10.1023/a:1004541830999

published in Journal of Statistical Physics 95(1-2), 367-392 (Springer Science+Business Media)

arxiv created 1998/12/18 · openalex publication_date 1999/04/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Common ground to recent studies exploiting relations between dynamical systems and non-equilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti-Cohen fluctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz-Spohn analysis of this fluctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the fluctuation theorem as a Gibbs property as it follows from the very definition of Gibbs state. We give a local version of the fluctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics.

Citations

• Chaotic dynamics, fluctuations, nonequilibrium ensembles
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory

Cited by

• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Possible extended forms of thermodynamic entropy
• Exact symmetries in the velocity fluctuations of a hot Brownian swimmer
• From dynamical systems to statistical mechanics: the case of the fluctuation theorem
• Non-equilibrium Dynamics, Thermalization and Entropy Production
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• Nonequilibrium fluctuations in a driven stochastic Lorentz gas
• Fluctuations of the heat exchanged between two quantum spin chains
• Absence of dissipation in trajectory ensembles biased by currents
• Fluctuation theorem, nonlinear response, and the regularity of time reversal symmetry
• Noncyclic and nonadiabatic geometric phase for counting statistics
• Posterior Probability and Fluctuation Theorem in Stochastic Processes
• Work relations for time-dependent states
• Thermoelectric phenomena via an interacting particle system
• Thermodynamics of a stochastic twin elevator
• Nonequilibrium thermodynamics at the microscale: Work relations and the second law
• The “footprints” of irreversibility
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields