Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics

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 analytical
function 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 a
continuous 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-differential
equation, 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-Mittal
entropic form.