FM 00-15;

Authors: Denis J. Evans, E. G. D. Cohen, Debra J. Searles, F. Bonetto

Title: Note on the Kaplan--Yorke dimension and linear transport coefficients.

Abstract:  number of new relations between the Kaplan--Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state.  A condition for the extensivity of phase space dimension reduction is given.  A new expression for the linear transport coefficients in terms of the Kaplan--Yorke dimension is derived.  Alternatively, the Kaplan--Yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system.  The agreement with computer simulations for an atomic fluid at small shear rates is very good.

Keywords:  dynamical systems, KY--dimension, Lyapunov exponent, transport coefficient.

Denis J. Evans: Research School of Chemistry, The Australian National University, Canberra, ACT 0200, Australia
E. G. D. Cohen: The Rockefeller University, 1230 York Avenue, New York, NY 10021
Debra J. Searles: School of Science, Griffith University, Nathan, Brisbane, Qld 4111, Australia
F. Bonetto: Department of Mathematics, Rutgers University, New Brunswick, NJ 08903