Self-organized criticality and thermodynamic formalism

Cessac B, Blanchard P, Krüger T, Meunier JL (2004)
JOURNAL OF STATISTICAL PHYSICS 115(5/6): 1283-1326.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We develop a thermodynamic formalism for a dissipative version of the Zhang model of Self-Organized Criticality, where a parameter allows us to tune the local energy dissipation. By constructing a suitable Markov partition we define Gibbs measures (in the sense of Sinai, Ruelle, and Bowen), partition functions, and topological pressure allowing the analysis of probability distributions of avalanches. We discuss the infinite-size limit in this setting. In particular, we show that a Lee-Yang phenomenon occurs in the conservative case. This suggests new connections to classical critical phenomena.
Stichworte
hyperbolic dynamical systems with; Lee-Yang singularity; self-organized criticality; thermodynamic formalism; singularities
Erscheinungsjahr
2004
Zeitschriftentitel
JOURNAL OF STATISTICAL PHYSICS
Band
115
Ausgabe
5/6
Seite(n)
1283-1326
ISSN
0022-4715
Page URI
https://pub.uni-bielefeld.de/record/1607863

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Cessac B, Blanchard P, Krüger T, Meunier JL. Self-organized criticality and thermodynamic formalism. JOURNAL OF STATISTICAL PHYSICS. 2004;115(5/6):1283-1326.
Cessac, B., Blanchard, P., Krüger, T., & Meunier, J. L. (2004). Self-organized criticality and thermodynamic formalism. JOURNAL OF STATISTICAL PHYSICS, 115(5/6), 1283-1326. doi:10.1023/B:JOSS.0000028057.16662.89
Cessac, B., Blanchard, P., Krüger, T., and Meunier, J. L. (2004). Self-organized criticality and thermodynamic formalism. JOURNAL OF STATISTICAL PHYSICS 115, 1283-1326.
Cessac, B., et al., 2004. Self-organized criticality and thermodynamic formalism. JOURNAL OF STATISTICAL PHYSICS, 115(5/6), p 1283-1326.
B. Cessac, et al., “Self-organized criticality and thermodynamic formalism”, JOURNAL OF STATISTICAL PHYSICS, vol. 115, 2004, pp. 1283-1326.
Cessac, B., Blanchard, P., Krüger, T., Meunier, J.L.: Self-organized criticality and thermodynamic formalism. JOURNAL OF STATISTICAL PHYSICS. 115, 1283-1326 (2004).
Cessac, B, Blanchard, Philippe, Krüger, Tyll, and Meunier, JL. “Self-organized criticality and thermodynamic formalism”. JOURNAL OF STATISTICAL PHYSICS 115.5/6 (2004): 1283-1326.