Entropy and Chaos in a Lattice Gas Cellular Automata

  • Franco Bagnoli
  • Raúl Rechtman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5191)


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.


Cellular Automaton Entropy Density Expansion Factor Large Lyapunov Exponent Marked Oscillation 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Franco Bagnoli
    • 1
  • Raúl Rechtman
    • 2
  1. 1.Dipartimento di EnergeticaUniversità di Firenze, Also CSDC and INFN, sez. FirenzeFirenzeItaly
  2. 2.Centro de Investigacíon en EnergíaUNAMTemixcoMexico

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