We consider the question of the existence of a generalized H-theorem in the context of the variational method in the information-theoretical approach that generates the nonequilibrium statistical operator formalism. After brie y reviewing how the latter provides mechano-statistical foundations for phenomenological irreversible thermodynamics, the socalled Informational Statistical Thermodynamic...

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Abstract: Entropy and its various generalizations are widely used in mathematical statistics, communication theory, physical and computer sciences for characterizing the amount of information in a probability distribution. We consider estimators of the quadratic Rényi entropy and some related characteristics of discrete and continuous probability distributions based on the number of coincident ...

A number of definitions of entropy in optics have both advantages and disadvantages. The major features of different entropy definitions are briefly characterized. The principal distinction between the statictics entropy definition and the thermodynamics one is indicated. The diffraction-caused radiation entropy is calculated.

Numerous entropy-type characteristics (functionals) generalizing Rényi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and distribution identification problems. We consider estimators of some entropy (integral) functionals for discrete and continuous distributions based on the numb...

A brief discussion is given of the traditional version of the Maximum Entropy Method, including a review of some of the criticism that has been made in regard to its use in statistical inference. Motivated by these questions, a modified version of the method is then proposed and applied to an example in order to demonstrate its use with a given time series.

Quantum gravity in 2+1 dimensions with a positive cosmological constant can be represented as an SL(2,C) Chern-Simons gauge theory. The symmetric vacuum of this theory is a degenerate configuration for which the gauge fields and spacetime metric vanish, while de Sitter space corresponds to a highly excited thermal state. Carlip’s approach to black hole entropy can be adapted in this context to ...

We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterizati...

Preface Science consists in using information about the world for the purpose of predicting , explaining, understanding, and/or controlling phenomena of interest. The basic difficulty is that the available information is usually insufficient to attain any of those goals with certainty. In these lectures we will be concerned with the problem of inductive inference , that is, the problem of reaso...

Degrees of belief are formed using observed evidence and statistical background information. In this paper we examine the process of how prior degrees of belief derived from the evidence are combined with statistical data to form more speciic degrees of belief. A statistical model for this process then is shown to vindicate the cross-entropy minimization principle as a rule for probabilistic de...