Statistical physics of temporal intermittency

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<2. On the other hand, for 2z, 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.