A consistent generalization of statistical mechanics is obtained by applying the MaxEnt principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging differential-functional equation yields a two-parameter class of generalized logarithms, from which entropies and power-law distributions follow: these distributions could be relevant in many anomalous systems. Within the specified range of parameters, these entropies possess positivity, continuity, symmetry, expansibility, decisivity, maximality, concavity, and are Lesche stable. The Boltzmann-Shannon entropy and some one parameter generalized entropies already known belong to this class. These entropies and their distribution functions are compared, and the corresponding deformed algebras are discussed.
Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics / KANIADAKIS G.; LISIA M; SCARFONE AM. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 71(2005), pp. 046128-046128. [10.1103/PhysRevE.71.046128]
|Titolo:||Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics|
|Data di pubblicazione:||2005|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1103/PhysRevE.71.046128|
|Appare nelle tipologie:||1.1 Articolo in rivista|