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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Thermodynamic entropy and chaos in a discrete hydrodynamical system
Franco Bagnoli1, Raúl Rechtman
1Dipartimento di Energetica, Università di Firenze, Via S. Marta 3, I-50139 Firenze, Italy. franco.bagnoli@unifi.it
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.
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