可加性細胞自動機上的熵

Abstract

本篇論文討論任意有限狀況的可加性細胞自動機(cellular automata)，並利用拓樸共軛(topological conjugate)與測度同構(measure isomorphic)的特性給予拓樸熵(topological entropy)及在伯努利測度(Bernoulli measure)下測度熵(measure-theoretic entropy)的公式。藉由拓樸熵與測度熵的公式能找到滿足變分原理(Variational Principle)的最大測度(maximum measure)，可用於物理的應用上。

In this paper we consider the additive cellular automata with any finite states, we take the properties of the topological conjugate and measure isomorphic to give a formula for topological entropy and measure-theoretic entropy with Bernoulli measure. After having the measure-theoretic entropy formula and the topological entropy formula, we can find the maximum measure such that satisfy the Variational Principle, and more apply in physics.