We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with special cases of modified Naudts’ φ-entropy. In a pioneering work sixty years ago, Jaynes [4] initiated the study of statistical physics by information theory. He...

We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q ↔ q−1 symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed. PACS: 05.20.-y; 0...

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This en-tropy is a variant of the generalized entropy of order α, considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Rényi, Tsallis, and Havrda-Charvát entropies. The generalized entropy measure introduced here is also shown to...

This is a concise introduction to the topic of nonextensive Tsallis statistics meant especially for those interested in its relation high energy proton-proton, proton-nucleus, and nucleus-nucleus collisions. The three types are reviewed. Only one them consistent with fundamental hypothesis equilibrium statistical mechanics. single particle distributions associated it, namely Boltzmann, Fermi-Di...

We show that there is an effect of nonextensivity acting upon the BCS model for superconductors in the ground state that motivates its study in the Tsallis’ statistical framework. We show that the weak-coupling limit superconductors are well described by q ∼ 1, where q is a real parameter which characterizes the degree of nonextensivity of the Tsallis’ entropy. Nevertheless, small deviations wi...

Abstract. The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being conducted with the help of statistical techniques. The pathway model, recently introduced by Mathai (2005), is utilized for thermonuclear functions ...

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...