Note on the Kaplan-Yorke Dimension and Linear Transport Coefficients

Abstract

A 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. The agreement with computer simulations for an atomic fluid at small shear rates is very good.