Possible physical meaning of the Tsallis entropy parameter.

Since the proposal of the Tsallis generalized entropy, the general explanation of the role played by the parameter q that defines which specific entropy to pick among a whole family, remained somewhat partial and tentative, although 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 fluctuations of a stochastic process, thus furnishing at least one of its possible physical origins.