We find a simple linear relation between the thermodynamic entropy and the largest Lyapunov exponent (LLE) of an discrete hydrodynamical system, a deterministic, two-dimensional lattice gas automaton (LGCA). This relation can be extended to irreversible processes considering the Boltzmann’s H function and the expansion factor of the LLE. The definition of LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems.
Entropy and Chaos in a Lattice Gas Cellular Automata / F. Bagnoli; R. Rechtman. - STAMPA. - 5191:(2008), pp. 120-127. (Intervento presentato al convegno 8th International Conference on Cellular Aotomata for Reseach and Industry, ACRI 2008 tenutosi a Yokohama, Japan nel September 23-26, 2008) [10.1007/978-3-540-79992-4_16].
Entropy and Chaos in a Lattice Gas Cellular Automata
BAGNOLI, FRANCO;
2008
Abstract
We find a simple linear relation between the thermodynamic entropy and the largest Lyapunov exponent (LLE) of an discrete hydrodynamical system, a deterministic, two-dimensional lattice gas automaton (LGCA). This relation can be extended to irreversible processes considering the Boltzmann’s H function and the expansion factor of the LLE. The definition of LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems.
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