2009/01/31 by Burhan Bakar, Uǧur Tırnaklı, Ugur Tirnakli · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.040103
published as Phys. Rev. E 79, 040103(R) (2009) · 5 pages, 6 eps figures, 1 bbl file; accepted for publication on PRE as a rapid communication, in press (2009)
arxiv created 2009/03/05 · openalex publication_date 2009/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The self-organized criticality in Ehrenfest's historical dog-flea model is analyzed by simulating the underlying stochastic process. The fluctuations around the thermal equilibrium in the model are treated as avalanches. We show that the distributions for the fluctuation length differences at subsequent time steps are in the shape of a q -Gaussian (the distribution which is obtained naturally in the context of nonextensive statistical mechanics) if one avoids the finite-size effects by increasing the system size. We provide clear numerical evidence that the relation between the exponent tau of avalanche size distribution obtained by maximum-likelihood estimation and the q value of appropriate q -Gaussian obeys the analytical result recently introduced by Caruso [Phys. Rev. E 75, 055101(R) (2007)]. This allows us to determine the value of q -parameter a priori from one of the well-known exponents of such dynamical systems.