The Tsallis entropy was proposed as a possible generalization of the standard Boltzmann-Gibbs-Shannon (BGS) entropy as a concept aimed at efficient characterisation of non-extensive complex systems. Ever since its introduction [1], it has been successfully applied in various fields [2]. In parallel, there have been numerous attempts to provide its formal derivation from an axiomatic foundation,...

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, Sα, for α ∈ (0, 1). We establish necessary and sufficient conditions for equality in the continuity bound and prove that these conditions are the same for every member of the family. Our result builds on recent work in which we constructed a st...

Francisco C. Alcaraz (a) and Constantino Tsallis (b,c) (a) Departamento de F́ısica, Universidade Federal de São Carlos, Via Washington Luiz, São Carlos-SP, Brazil (b) Centro Brasileiro de Pesquisas F́ısicas, Xavier Sigaud 150, 22290-180, Rio de Janeiro-RJ, Brazil ([email protected]) (c) Erwin Schroedinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien, Austria (Febr...

This note presents explicitly a strong connection between the Tsallis thermodynamics and the so-called prospect theory introduced to take into account agent’s decisions under risk. Moreover, using the cumulative prospect theory adapted here for a continuous framework, we show that if the Tsallis parameter q belongs to the interval [0,1], then the prospect theory requirement that extreme events ...

Superstatistics is a ‘statistics of a statistics’ relevant for driven nonequilibrium systems with fluctuating intensive parameters. It contains Tsallis statistics as a special case. We show that probability density functions of velocity differences and accelerations measured in Eulerian and Lagrangian turbulence experiments are well reproduced by simple superstatistics models. We compare fits o...

The four dimensional pure compact U(1) gauge theory is known to posses a phase transition (PT) separating a confined phase and a Coulomb one and the determination of the order of PT is of great importance. In the pure compact U(1) gauge theory, however, the determination of the order of PT is very difficult since on large lattices the standard updating algorithms like Metropolis, heat-bath, hyb...

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for ...