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Nonlinear Sciences > Cellular Automata and Lattice Gases
Title: Classification of Cellular Automata based on Statistical Mechanics
(Submitted on 15 Nov 2022 (v1), last revised 11 May 2023 (this version, v2))
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.
Submission history
From: Andrea Idini [view email][v1] Tue, 15 Nov 2022 14:21:31 GMT (1779kb,D)
[v2] Thu, 11 May 2023 14:34:30 GMT (1788kb,D)
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