Family of additive entropy functions out of thermodynamic limit

Details Family of additive entropy functions out of thermodynamic limit Family of additive entropy functions out of thermodynamic limit

2002-05-24

arxiv.org/abs/cond-mat/0205511v1

PHYSICAL REVIEW E 67 (2003), 016104

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.67.016104

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. An example of how longer tails are described within the present approach is worked out for the canonical ensemble. In addition, we discuss a possible origin of a hidden statistical dependence, and give explicit recipes how to construct corresponding generalizations of master equation.

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