Astrophysical Thermonuclear Functions for Boltzmann-Gibbs Statistics and Tsallis Statistics

Generalized Additive Entropies in Fully Developed Turbulence

We explore a possible application of the additive generalization of the Boltzmann-Gibbs-Shannon entropy proposed in [A.N. Gorban, I.V. Karlin, Phys. Rev. E, 67:016104 (2003)] to fully developed turbulence. The predicted probability distribution functions are compared with those obtained from Tsallis' entropy and with experimental data. Consequences of the existence of hidden subsystems are illustrated.

Group entropies, correlation laws and zeta functions

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 dic…

Statistical mechanics and thermodynamics of complex systems

An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization of (classical) Boltzmann-Gibbs thermostatistics is suggested and connected to recent nonextensive statistics formulations. This is accomplished by defining a convenient squeezing function which restricts among the collections of Boltzmann-Gibbs configurations of the complete equilibrium closure. The formalism embodies Beck-Cohen superstatistics and a direct …

广义玻尔兹曼-盖布斯分布与电子配分函数悖论

Generalized Boltzmann-Gibbs Distribution and the Electronic Partition Function Paradox

本文提出广义玻尔兹曼-盖布斯分布，通过非加性熵解决电子配分函数悖论，并展示其在不同能量谱下的热力学行为。