Linear response theory reformulated from the chaotic dynamics

Nobuhiko Sait̂o, Yasushi Matsunaga

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    Inadequacy of perturbation treatment in chaotic dynamics is pointed out, especially for phase space distribution function. The coarse graining is introduced into phase space distribution function for describing macroscopic thermodynamic process as a necessary and inevitable procedure for the transition from microscopic to macroscopic levels. A concept of convergence in law is employed for coarse graining. Thus a new approach to the linear response theory is presented, which can remove the various difficulties in the conventional linear response theory. The derivation of the distribution function in the sense of convergence in law is left open, but it is expected that the principal results such as fluctuation-dissipation theorem, Kubo formula for kinetic coefficient remain valid, provided that an appropriate interpretation is applied. Furthermore the entropy is shown to increase and the susceptibility derived in this theory is adiabatic susceptibility expected as a thermodynamic process. The present formulation will provide an answer to the critical discussion by van Kampen.

    Original languageEnglish
    Pages (from-to)3089-3105
    Number of pages17
    JournalJournal of the Physical Society of Japan
    Issue number9
    Publication statusPublished - 1989 Sep



    • Chaotic dynamics
    • Coarse graining
    • Convergence in law
    • Entropy
    • Fluctuation-dissipation theorem
    • Green-Kubo formula
    • Liouville equation
    • Susceptibilities

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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