Statistical equilibrium in deterministic cellular automata

TL;DR

This paper explores how certain deterministic cellular automata naturally evolve towards equilibrium states of maximal disorder, aligning with thermodynamic principles, and offers a Boltzmann-inspired statistical explanation.

Contribution

It introduces a statistical scheme for understanding equilibrium in cellular automata, providing a rigorous, combinatorial framework inspired by Boltzmann's ideas.

Findings

Cellular automata can exhibit thermodynamic-like behavior.

A combinatorial statistical scheme explains the approach to equilibrium.

Probabilistic interpretation avoids subjective biases.

Abstract

Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal disorder. This chapter is an exposition of this phenomenon and of a statistical scheme for its explanation. The formulation is in the same vein as Boltzmann's ideas, but the simple combinatorial setup offers clarification and hope for generic mathematically rigorous results. Probabilities represent frequencies and subjective interpretations are avoided.