Quasicanonical Gibbs distribution and Tsallis nonextensive statistics

Abstract

We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and thermodynamics, with Tsallis parameter q is found to be related to the number of particles in the quasithermostat. We show that the chi-square distribution of fluctuating temperature used recently by Beck can be partially understood in terms of normal random momenta of particles in the quasithermostat. Also, we discuss on the importance of the time scale hierarchy and fluctuating probability distribution functions in understanding of Tsallis distribution, within the framework of kinetics of dilute gas and weakly inhomogeneous systems.

22 pages, 1 eps-figure

References in corpus (18)

• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Dynamical foundations of nonextensive statistical mechanics
• Nonextensive thermodynamic relations
• Axioms and uniqueness theorem for Tsallis entropy
• General pseudoadditivity of composable entropy prescribed by existence of equilibrium
• Nonadditive conditional entropy and its significance for local realism
• Implications of Form Invariance to the Structure of Nonextensive Entropies
• Generalized entropies from first principles
• On the small-scale statistics of Lagrangian turbulence
• Non-additivity of Tsallis entropies and fluctuations of temperature
• Multi-parameter generalization of nonextensive statistical mechanics
• Generalized statistical mechanics and fully developed turbulence
• Nonuniqueness of Canonical Ensemble Theory arising from Microcanonical Basis
• Justification of Power-Law Canonical Distributions Based on Generalized Central Limit Theorem
• Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions
• An interpretation of Tsallis statistics based on polydispersity
• BRST Approach to Hamiltonian Systems
• Statistical Mechanical Foundations for Systems with Nonexponential Distributions

Cited by in corpus (12)

• Classical small systems coupled to finite baths
• One-dimensional Langevin models of fluid particle acceleration in developed turbulence
• Non-Gaussian PDFs from Maximum-Entropy-principle considerations
• The PDF of fluid particle acceleration in turbulent flow with underlying normal distribution of velocity fluctuations
• Information theory approach (extensive and nonextensive) to high energy multiple production processes
• Conditional Lagrangian acceleration statistics in turbulent flows with Gaussian distributed velocities
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Stochastic models of Lagrangian acceleration of fluid particle in developed turbulence
• Thermodynamics arising from Tsallis' thermostatistics
• Skewness of probability density functions of fluid particle acceleration in developed turbulence
• Phenomenological Gaussian screening in the nonextensive statistics approach to fully developed turbulence
• The conditional mean acceleration of fluid particle in developed turbulence