Square Entropy and Uniform n-to-1 Bernoulli Transformations

2025/05/30 by Pouya Mehdipour, Mehdipour, Pouya, Shaldehi, Somayeh Jangjooye
Mathematics · Physics and Astronomy · #Statistical and numerical algorithms #Advanced Optimization Algorithms Research #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2505.24647

Abstract

In this paper, we define the so-called square entropy and prove that n-to-1 full zip shift maps are intrinsically ergodic. Furthermore, we show that square entropy characterizes uniform n-to-1 transformations of (m,l)-Bernoulli type that are extended Bernoulli transformations.

Citations

• Zip shift Space
• Uniform endomorphisms which are isomorphic to a Bernoulli shift
• Some systems with unique equilibrium states

Related

• Smooth mixing transformations with loosely Bernoulli cartesian product
• A monotone isomorphism theorem
• Entropy and the Uniform Mean Ergodic Theorem for a Family of Sets
• Uniform endomorphisms which are isomorphic to a Bernoulli shift
• Lecture notes on ergodic transformations