Determinism and thermodynamics: Ising cellular automata
A. B. MacIsaac, D. L. Hunter, Martin J. Corsten, Naeem Jan · Physical Review A · 1991
Determinism with or without reversibility and the part of it plays in thermodynamics is poorly understood and rarely explored. To investigate the effects of determinism we introduce a class of cellular automata whose rules are constructed from the Boltzmann probabilities of the Ising model. This class of Ising cellular automata (ICA) has as its high-temperature limit the well-studied Kauffman model [S. A. Kauffman, J. Theor. Biol. 22, 437 (1969); Physica D 10, 145 (1984)]. The control of determinism allows us to establish a direct connection between the Kauffman model and percolation and between correlated percolation and these ICA's. A comparison of the chaotic properties offers an informative look at the consequences of determinism. A line of critical points exists between the ``frozen'' and ``chaotic'' phases for ICA, and the zero-field critical temperature is approximately twice that of the Ising model.