2002 -06 -19
10 :15 at ML J 21

Family of additive entropy functions out of thermodynamic limit

Alexander Gorban

Institute of Polymers, ETH Zurich

Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description of certain effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from Tsallis entropies, and is essentially a convex combination of the Boltzmann-Gibbs-Shannon entropy and the entropy function introduced by Burg. Generalized canonical ensembles are constructed explicitly which makes operations within the present formalism as efficient as in the case of BGS entropy. Examples of how longer and shorter tails are described within the present approach are discussed.