Thermodynamics in Stochastic Conway’s Game of Life

Abstract

Cellular automata can simulate many complex physical phenomena using the power of simple rules. The presented methodological platform expresses the concept of programmable matter, of which Newton’s laws of motion are an example. Energy is introduced as the equivalent of the “Game of Life” mass, which can be treated as the first level of approximation. The temperature presence and propagation was calculated for various lattice topologies and boundary conditions, using the Shannon entropy measure. This study provides strong evidence that, despite the principle of mass and energy conservation not being fulfilled, the entropy, mass distribution, and temperature approach thermodynamic equilibrium. In addition, the described cellular automaton system transitions from a positive to a negative temperature, which stabilizes and can be treated as a signature of a system in equilibrium. The system dynamics is presented for a few species of cellular automata competing for maximum presence on a given lattice with different boundary conditions.