View article

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution p_i by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. Indeed, the Maxwell-Boltzmann distribution is obtained by maximizing the Boltzmann-Shannon entropy under proper constraints. The second link is algebraic and imposes that both the entropy and the distribution must be expressed in terms of the same function in direct and inverse form. Indeed, the Maxwell-Boltzmann distribution p_i is expressed in terms of the exponential function, while the Boltzmann-Shannon entropy is defined as the mean value of -ln (p_i). In generalized statistical mechanics the second link is customarily relaxed. Of course, the generalized exponential function defining the probability distribution function after inversion, produces a generalized logarithm Λ(p_i). But …