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Diffusion on fractal phase spaces and entropy production

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  • Lemke, N
  • de Almeida, R.M.C

Abstract

Complex systems may show strongly non-exponential relaxation, the origins of these behavior seem to be related to the fractal structure of the phase space. In this article, we consider the diffusion on a dilute hypercube, this stochastic process is a coarse-grained model for the time evolution of a glassy system, where both the dynamics and the structure of the phase space was considered as simple as possible. We characterize this process using two quantities: a memory function and the Tsallis entropy. The first one is a measure of mixing while the second is related to non-extensivity. We characterize quantitatively their relationship. Finally, we discuss the implications for other glassy and complex systems.

Suggested Citation

  • Lemke, N & de Almeida, R.M.C, 2004. "Diffusion on fractal phase spaces and entropy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 309-315.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:309-315
    DOI: 10.1016/j.physa.2004.04.021
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    References listed on IDEAS

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    1. Lemke, N. & de Almeida, R.M.C., 2003. "Tsallis entropy production for diffusion on the diluted hypercube," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(3), pages 396-408.
    2. Pablo G. Debenedetti & Frank H. Stillinger, 2001. "Supercooled liquids and the glass transition," Nature, Nature, vol. 410(6825), pages 259-267, March.
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