The weighed average geodetic of distributions of probabilities in the statistical physics

TL;DR

This paper applies geometric methods from statistical decision theory to derive expressions for the nonequilibrium statistical operator and superstatistics, unifying these concepts through the framework of weighted average geodetics.

Contribution

It introduces a novel geometric approach to statistical physics by connecting decision rule geometry with nonequilibrium statistical operators and superstatistics.

Findings

Derived expressions for nonequilibrium statistical operator.

Unified superstatistics within the geometric framework.

Extended the application of decision rule geometry to statistical physics.

Abstract

The results received in works [Centsov N.N. [N.N. Chentsov], Statistical decision rules and optimal inference, 1982 Amer. Math. Soc. (Translated from Russian); Morozova, E. A., Chentsov, N. N. Natural geometry of families of probability laws. 1991 Probability theory, 8, 133--265, 270--274, 276 (in Russian)] for statistical distributions at studying algebra of decision rules and natural geometry generated by her, are applied to estimations of the nonequilibrium statistical operator and superstatistics. Expressions for the nonequilibrium statistical operator and superstatistics are received as special cases of the weighed average geodetic of distributions of probabilities.