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 thispaper, 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 analyticalfunction f{p}(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 acontinuous deformation of the multinomial coefficients depending on a set of deformation parameters {p}. It is shown that, when f{p}(n) is related to the solutions of a simple linear difference-differentialequation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (k, r) known, in the framework of the information theory, as Sharma-Taneja-Mittalentropic form.
Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics
Antonio Maria Scarfone
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 thispaper, 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 analyticalfunction f{p}(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 acontinuous deformation of the multinomial coefficients depending on a set of deformation parameters {p}. It is shown that, when f{p}(n) is related to the solutions of a simple linear difference-differentialequation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (k, r) known, in the framework of the information theory, as Sharma-Taneja-Mittalentropic form.File | Dimensione | Formato | |
---|---|---|---|
prod_462633-doc_180856.pdf
accesso aperto
Descrizione: Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics
Tipologia:
Versione Editoriale (PDF)
Licenza:
Creative commons
Dimensione
379.32 kB
Formato
Adobe PDF
|
379.32 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.