Self-Organized Criticality and Thermodynamic formalism

Details Self-Organized Criticality and Thermodynamic formalism Self-Organized Criticality and Thermodynamic formalism

2002-09-19

arxiv.org/abs/nlin/0209038v1

Journal of Statistical Physics, Vol. 115, No 516, 1283-1326 (2004).

Nonlinear Sciences

Chaotic Dynamics

35 pages, 15 Figures, submitted

Scientific paper

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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