Analysis of relationships between spectral potential of transfer operators, $t$-entropy, entropy and topological pressure

TL;DR

This paper explores the connections between spectral properties of transfer operators and fundamental concepts in information theory and thermodynamics, providing explicit formulas linking these areas in dynamical systems.

Contribution

It introduces explicit formulas linking spectral potential, $t$-entropy, and topological pressure, highlighting the roles of inverse rami-rate and forward entropy in dynamical systems.

Findings

Derived explicit formulas connecting spectral potential and $t$-entropy.

Identified the significance of inverse rami-rate and forward entropy.

Analyzed the impact of non-contractibility on spectral characteristics.

Abstract

The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism (entropy and topological pressure). We present explicit formulae linking these objects with $t$-entropy and spectral potential. Herewith we uncover the role of inverse rami-rate, forward entropy along with essential set and the property of non-contractibility of a dynamical system.