Partially observable systems and quotient entropy via graphs

TL;DR

This paper extends entropy theory to partially observable dynamical systems using graph-based symbolic coding, introducing quotient-topological entropy and exploring its structure and computation methods.

Contribution

It introduces quotient-topological entropy for partially observable systems and links entropy computation to graph theory via Markov partitions.

Findings

Quotient-topological entropy can be explicitly computed using symbolic coding.

A functorial extension of entropy theory to partially observable systems is established.

The relationship between dynamical systems and graphs facilitates entropy analysis.

Abstract

We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We show how quotient entropy can be explicitly computed by symbolic coding. To do so, we make use of the relationship between the category of dynamical systems and the category of graphs, a connection mediated by Markov partitions and topological Markov chains.