We show that the thermodynamic entropy density is proportional to the largest Lyapunov exponent (LLE) of a discrete hydrodynamical system, a deterministic two-dimensional lattice gas automaton. The definition of the LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems. This relation is justified using a Markovian model. In an irreversible process with an initial density difference between both halves of the system, we find that Boltzmann's H function is linearly related to the expansion factor of the LLE although the latter is more sensitive to the presence of traveling waves.

Thermodynamic entropy and chaos in a discrete hydrodynamical system / F. Bagnoli; R. Rechtman. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - STAMPA. - 79:(2009), pp. 041115-041121. [10.1103/PhysRevE.79.041115]

Thermodynamic entropy and chaos in a discrete hydrodynamical system

BAGNOLI, FRANCO;
2009

Abstract

We show that the thermodynamic entropy density is proportional to the largest Lyapunov exponent (LLE) of a discrete hydrodynamical system, a deterministic two-dimensional lattice gas automaton. The definition of the LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems. This relation is justified using a Markovian model. In an irreversible process with an initial density difference between both halves of the system, we find that Boltzmann's H function is linearly related to the expansion factor of the LLE although the latter is more sensitive to the presence of traveling waves.
79
041115
041121
F. Bagnoli; R. Rechtman
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/358492
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