Note on the Kaplan-Yorke dimension and linear transport coefficients

Denis J. Evans; E. G.D. Cohen; Debra J. Searles; F. Bonetto

doi:10.1023/a:1026449702528

Note on the Kaplan-Yorke dimension and linear transport coefficients

Denis J. Evans^*, E. G.D. Cohen, Debra J. Searles, F. Bonetto

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

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.

Original language	English
Pages (from-to)	17-34
Number of pages	18
Journal	Journal of Statistical Physics
Volume	101
Issue number	1-2
DOIs	https://doi.org/10.1023/a:1026449702528
Publication status	Published - Oct 2000

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title = "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.",

keywords = "Dynamical systems, KY-dimension, Lyapunov exponent, Transport coefficient",

author = "Evans, {Denis J.} and Cohen, {E. G.D.} and Searles, {Debra J.} and F. Bonetto",

year = "2000",

month = oct,

doi = "10.1023/a:1026449702528",

language = "English",

volume = "101",

pages = "17--34",

journal = "Journal of Statistical Physics",

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T1 - Note on the Kaplan-Yorke dimension and linear transport coefficients

AU - Evans, Denis J.

AU - Cohen, E. G.D.

AU - Searles, Debra J.

AU - Bonetto, F.

PY - 2000/10

Y1 - 2000/10

N2 - 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.

AB - 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.

KW - Dynamical systems

KW - KY-dimension

KW - Lyapunov exponent

KW - Transport coefficient

UR - http://www.scopus.com/inward/record.url?scp=0034288333&partnerID=8YFLogxK

U2 - 10.1023/a:1026449702528

DO - 10.1023/a:1026449702528

M3 - Article

SN - 0022-4715

VL - 101

SP - 17

EP - 34

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

Note on the Kaplan-Yorke dimension and linear transport coefficients

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