Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

P. Gaspard; J. R. Dorfman; .

doi:10.1103/physreve.52.3525

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arXiv · chao-dyn/9504014

Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

P. Gaspard·J. R. Dorfman·.

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Abstract

The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.

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P. Gaspard, J. R. Dorfman, .. 1995-04-26. Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients. https://doi.org/10.1103/physreve.52.3525

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