DESCRIPTION OF PROBABILISTICAL SYSTEMS WITH STRONGLY STATISTICALLY DEPENDENT ELEMENTS

Abstract

We propose the f-divergences of two probability distributions as the measures of the organization of a probabilistic system with respect to its probabilistic uncertainty. A probabilistic system consist of stochastical objects on which random variables are defined which are statistically dependent. Using Shannon's f-divergence for the organization of a probabilistic system we express it in terms of the probability distributions of the element random variables and their statistical linkages. Then we find the maximum entropy of a probabilistic system if the statistical linkages between its elements are given as input data. We show that an important class of physical statistical systems can be described by the probabilistic systems of Gibbsian type.

INDEX TERM:

• Probabilistic system
• f-divergence of two probability distributions
• configurational organization
• probabilistic uncertainty
• maximum entropy
• physical statistical systems.