Thermodynamic phase transitions for Pomeau-Manneville maps

Abstract

We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a distributional limit theorem to provide both a powerful tool for calculating thermodynamic potentials as also an understanding of the dynamic characteristics at each instability phase. In particular, topological pressure and Renyi entropy are calculated exactly for such systems. Finally, we show the connection of the distributional limit theorem with non-Gaussian fluctuations of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad. Sci. USA 85, 4591 (1988)].

5 pages

References in corpus (2)

• Exact and explicit probability densities for one-sided Levy stable distributions
• Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions

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