Group entropies, correlation laws and zeta functions

Abstract

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.

to appear in Physical Review E

References in corpus (6)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Thermostatistics of overdamped motion of interacting particles
• Maximum entropy principle and power-law tailed distributions
• Landau levels and Riemann zeros
• Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation
• Robustness of the second law of thermodynamics under generalizations of the maximum entropy method

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