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Entropy 2012, 14(5), 924-944; doi:10.3390/e14050924
Article

Entropy Concept for Paramacrosystems with Complex States

Institute for Systems Analysis, Russian Academy of Sciences, 9, prospekt 60-let Octyabrya, Moscow, 117312, Russia
Received: 23 February 2012 / Revised: 18 April 2012 / Accepted: 26 April 2012 / Published: 10 May 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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Abstract

Consideration is given to macrosystems called paramacrosystems with states of finite capacity and distinguishable and undistinguishable elements with stochastic behavior. The paramacrosystems fill a gap between Fermi and Einstein macrosystems. Using the method of the generating functions, we have obtained expressions for probabilistic characteristics (distribution of the macrostate probabilities, physical and information entropies) of the paramacrosystems. The cases with equal and unequal prior probabilities for elements to occupy the states with finite capacities are considered. The unequal prior probabilities influence the morphological properties of the entropy functions and the functions of the macrostate probabilities, transforming them in the multimodal functions. The examples of the paramacrosystems with two-modal functions of the entropy and distribution of the macrostate probabilities are presented. The variation principle does not work for such cases.
Keywords: entropy; macrosystems; paramacrosystems; generating functions; variational principle entropy; macrosystems; paramacrosystems; generating functions; variational principle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Popkov, Y.S. Entropy Concept for Paramacrosystems with Complex States. Entropy 2012, 14, 924-944.

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