Self-Organized Criticality and Thermodynamic formalism

Abstract : We introduce a dissipative version of the Zhang's model of Self-Organized Criticality, where a parameter allows to tune the local energy dissipation. We analyze the main dynamical features of the model and relate in particular the Lyapunov spectrum with the transport properties in the stationary regime. We develop a thermodynamic formalism where we define formal Gibbs measure, partition function and pressure characterizing the avalanche distributions. We discuss the infinite size limit in this setting. We show in particular that a Lee-Yang phenomenon occurs in this model, for the only conservative case. This suggests new connexions to classical critical phenomena.
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https://hal.inria.fr/inria-00529555
Contributeur : Bruno Cessac <>
Soumis le : lundi 25 octobre 2010 - 20:37:08
Dernière modification le : vendredi 12 janvier 2018 - 01:55:32

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B. Cessac, Ph. Blanchard, T. Krueger, J. L. Meunier. Self-Organized Criticality and Thermodynamic formalism. Journal of Statistical Physics, Springer Verlag, 2002, 115 (5-6), pp.1283-1326. 〈10.1023/B:JOSS.0000028057.16662.89〉. 〈inria-00529555〉

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