Next Article in Journal
Applying Multiscale Entropy to the Complexity Analysis of Rainfall-Runoff Relationships
Next Article in Special Issue
Adaptive Computation of Multiscale Entropy and Its Application in EEG Signals for Monitoring Depth of Anesthesia During Surgery
Previous Article in Journal / Special Issue
An Entropic Estimator for Linear Inverse Problems
Article Menu

Export Article

Open AccessArticle
Entropy 2012, 14(5), 924-944;

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)
Full-Text   |   PDF [1638 KB, uploaded 24 February 2015]   |  


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. View Full-Text
Keywords: entropy; macrosystems; paramacrosystems; generating functions; variational principle entropy; macrosystems; paramacrosystems; generating functions; variational principle

Figure 1

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top