Maximum Renyi entropy principle for systems with power--law Hamiltonian

Details Maximum Renyi entropy principle for systems with power--law Hamiltonian Maximum Renyi entropy principle for systems with power--law Hamiltonian

2004-02-16

arxiv.org/abs/cond-mat/0402404v3

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 7 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.93.130601

The Renyi distribution ensuring the maximum of a Renyi entropy is investigated for a particular case of a power--law Hamiltonian. Both Lagrange parameters, $\alpha$ and $\beta$ can be excluded. It is found that $\beta$ does not depend on a Renyi parameter $q$ and can be expressed in terms of an exponent $\kappa$ of the power--law Hamiltonian and an average energy $U$. The Renyi entropy for the resulted Renyi distribution reaches its maximal value at $q=1/(1+\kappa)$ that can be considered as the most probable value of $q$ when we have no additional information on behaviour of the stochastic process. The Renyi distribution for such $q$ becomes a power--law distribution with the exponent $-(\kappa +1)$. When $q=1/(1+\kappa)+\epsilon$ ($0<\epsilon\ll 1$) there appears a horizontal "head" part of the Renyi distribution that precedes the power--law part. Such a picture corresponds to observables.

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