Thermodynamic entropy and chaos in a discrete hydrodynamical system.

Phys Rev E Stat Nonlin Soft Matter Phys

Dipartimento di Energetica, Università di Firenze, Via S. Marta 3, I-50139 Firenze, Italy.

Published: April 2009

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.

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http://dx.doi.org/10.1103/PhysRevE.79.041115DOI Listing

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