As known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain ana-lytical function f{π} (n) of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters {π}. It is shown that, when f{π} (n) is related to the solutions of a simple linear difference–differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (κ, r) known, in the framework of the information theory, as Sharma–Taneja–Mittal entropic form.

Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics / Scarfone, A. M.. - In: ENTROPY. - ISSN 1099-4300. - ELETTRONICO. - 24:2(2022), p. 140. [10.3390/e24020140]

Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics

Scarfone A. M.
2022

Abstract

As known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain ana-lytical function f{π} (n) of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters {π}. It is shown that, when f{π} (n) is related to the solutions of a simple linear difference–differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (κ, r) known, in the framework of the information theory, as Sharma–Taneja–Mittal entropic form.
2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2954075