Statistical physics of temporal intermittency

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Abstract
The thermodynamic formalism for dynamical systems is applied to a class of mappings of ‘‘laminar-turbulent’’ temporal intermittency. The corresponding statistical system is shown to be a lattice gas with many-body interactions of clustering type. This one-dimensional system bears a close analogy with the Fisher-Felderhof droplet model of condensation. The abnormal dynamic fluctuations give rise to a phase transition. The critical behaviors, which depend solely on the characteristic exponent z of the original map, are studied analytically, and a number of unexpected results are obtained. In the pressure-temperature plane, the intermittant state is located on a critical line that separates the chaotic (‘‘turbulent’’) state from the periodic (‘‘laminar’’) state. The transition from one phase to the other may be of first order if z. On the other hand, for 2≤z, the ‘‘sporadic state’’ introduced by Gaspard and Wang [Proc. Natl. Acad. Sci. U.S.A. 85, 4591 (1988)] is existent and corresponds to a codimension-two point on the critical curve.

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