Possible physical meaning of the Tsallis entropy parameter - art. no. 036125

Since the proposal of the Tsallis generalized entropy, the general explanat ion of the role played by the parameter q that defines which specific entro py to pick among a whole family, remained somewhat partial and tentative, a lthough some particular examples were taken into account specifically. The purpose of the present paper is to present a rigorous formal derivation of a mathematical expression giving the parameter q in terms of the momentum f luctuations of a stochastic process, thus furnishing at least one of its po ssible physical origins.