Variational principles for t-entropy, the spectral potential of transfer operator, and entropy statistic theorem are equivalent

TL;DR

This paper demonstrates the equivalence of variational principles related to t-entropy, spectral potential, and entropy statistic theorem for transfer operators, providing new proofs for these fundamental concepts.

Contribution

It establishes the equivalence of key variational principles for transfer operators and offers new proofs for these foundational results.

Findings

Proves the equivalence of variational principles for t-entropy, spectral potential, and entropy statistic theorem.

Provides new proofs for the established equivalences.

Enhances understanding of transfer operator spectral theory.

Abstract

For any transfer operator we establish the equivalence of variational principles for $t$-entropy, the spectral potential and entropy statistic theorem and give new proofs for all these statements.