The q-exponential family in statistical physics

Abstract

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.

18 pages, 4 figures, proceedings of SigmaPhi 2008

References in corpus (9)

• Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory
• Temperature of nonextensive system: Tsallis entropy as Clausius entropy
• A generalization of the central limit theorem consistent with nonextensive statistical mechanics
• Generalized entropy optimized by an arbitrary distribution
• Escort--Husimi distributions, Fisher information and nonextensivity
• Scale invariance and related properties of q-Gaussian systems
• Parameter estimation in nonextensive thermostatistics
• Power-Law distributions and Fisher's information measure
• Entropies for complex systems: generalized-generalized entropies

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• On multidimensional generalized Cramér-Rao inequalities, uncertainty relations and characterizations of generalized $q$-Gaussian distributions
• Data Set Models and Exponential Families in Statistical Physics and Beyond
• Non-extensivity of the configurational density distribution in the classical microcanonical ensemble
• Bistable stochastic processes in the q-exponential family
• The exponential family in abstract information theory
• Statistical Einstein manifolds of exponential families with group-invariant potential functions
• Sparse Continuous Distributions and Fenchel-Young Losses
• q-Paths: Generalizing the Geometric Annealing Path using Power Means
• On Voronoi diagrams and dual Delaunay complexes on the information-geometric Cauchy manifolds