Subshifts of finite type which have completely positive entropy

TL;DR

This paper constructs a specific subshift of finite type based on domino tilings, demonstrating it has completely positive entropy with a unique measure of maximal entropy, but it is not equivalent to a Bernoulli shift.

Contribution

It introduces a new subshift of finite type derived from domino tilings that exhibits completely positive entropy without being Bernoulli, expanding understanding of entropy in dynamical systems.

Findings

The subshift has a measure of maximal entropy.

It exhibits completely positive entropy.

It is not isomorphic to a Bernoulli shift.

Abstract

Domino tilings have been studied extensively for both their statistical properties and their dynamical properties. We construct a subshift of finite type using matching rules for several types of dominos. We combine the previous results about domino tilings to show that our subshift of finite type has a measure of maximal entropy with which the subshift has completely positive entropy but is not isomorphic to a Bernoulli shift.