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Thermodynamics of Small Systems Through a Reversible and Conservative Discrete Automaton

Part of the Emergence, Complexity and Computation book series (ECC,volume 42)


The Q2R model is a cellular automaton which is a dynamical variation of the Ising model for ferromagnetism that possesses quite rich and complex dynamics. It has the property of being conservative and reversible but, in practice, it shows irreversible behavior for relatively small system sizes. In this work we review some of its main properties and use it to simulate de behavior of a classical model for irreversible thermodynamical systems: the Ehrenfest’s dog-flea model.


  • Fixed point
  • Cycle
  • Cellular automata

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  • DOI: 10.1007/978-3-030-92551-2_13
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  1. 1.

    Other dynamical invariants are known in the literature [10].


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Correspondence to Sergio Rica .

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Montalva-Medel, M., Rica, S., Urbina, F. (2022). Thermodynamics of Small Systems Through a Reversible and Conservative Discrete Automaton. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham.

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