Classification of Cellular Automata based on Statistical Mechanics

TL;DR

This paper introduces a method to classify two-dimensional cellular automata based on their thermodynamic properties, linking their behavior to physical systems like ideal gases, and demonstrating the approach's robustness.

Contribution

It applies statistical mechanics and thermodynamics to classify cellular automata, providing a novel framework for understanding their physical analogs.

Findings

Thermodynamic variables effectively differentiate cellular automata behaviors.

The classification predicts properties of cellular automata rules.

The approach is robust across different rule sets.

Abstract

Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work, statistical mechanics and thermodynamics are used to analyse a large set of outer totalistic two-dimensional cellular automata. Thermodynamic variables and potentials are derived and computed according to three different approaches to determine if a cellular automaton rule is representing a system akin to the ideal gas, in or out of the thermodynamical equilibrium. It is suggested that this classification is sufficiently robust and predictive of interesting properties for particular set of rules.