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Role of ergodicity in the transient Fluctuation Relation and a new relation for a dissipative non-chaotic map

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  • Adamo, Paolo A.
  • Colangeli, Matteo
  • Rondoni, Lamberto

Abstract

Toy model dynamical systems, such as the baker maps, are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of reversibility, with peculiar basins of attraction and steady states. In particular, we test the conditions required for the validity of the transient Fluctuation Relation. Our analysis illustrates by means of concrete examples why ergodicity of the equilibrium dynamics (also known as “ergodic consistency”) seems to be a necessary condition for the transient Fluctuation Relation. This investigation then leads to the numerical verification of a kind of transient relation which, differently from the usual transient Fluctuation Relation, holds only asymptotically. At the same time, this relation is not a steady state Fluctuation Relation, because the steady state is a fixed point without fluctuations.

Suggested Citation

  • Adamo, Paolo A. & Colangeli, Matteo & Rondoni, Lamberto, 2016. "Role of ergodicity in the transient Fluctuation Relation and a new relation for a dissipative non-chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 54-66.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:54-66
    DOI: 10.1016/j.chaos.2015.11.025
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    1. C. P. Dettmann & E. G. D. Cohen & H. van Beijeren, 1999. "Microscopic chaos from brownian motion?," Nature, Nature, vol. 401(6756), pages 875-875, October.
    2. Gallavotti, Giovanni, 1999. "A local fluctuation theorem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 39-50.
    3. Kraichnan, Robert H., 2000. "Deviations from fluctuation–relaxation relations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 30-36.
    4. Howard Lee, M., 2006. "Why does Boltzmann's ergodic hypothesis work and when does it fail," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 150-154.
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