Sofic measure entropy via finite partitions

TL;DR

This paper introduces a new way to compute sofic measure entropy without generators, using finite partitions, and provides a method to calculate entropy for Bernoulli actions efficiently.

Contribution

It offers a generator-free formulation of sofic measure entropy and extends Bowen's finite base case approach to general Bernoulli actions.

Findings

Provides a Kolmogorov-Sinai theorem for sofic measure entropy

Develops a concise computation method for Bernoulli actions

Establishes a generator-free approach to entropy calculation

Abstract

We give a generator-free formulation of sofic measure entropy using finite partitions and establish a Kolmogorov-Sinai theorem. We also show how to compute the values for general Bernoulli actions in a concise way using the arguments of Bowen in the finite base case.