Abstract
Nonequilibrium systems in thermodynamic steady states can be studied by computer simulation, and the calculated transport coefficients are in agreement with results obtained by equilibrium methods. The basic algorithms are discussed. Although they require the incorporation of a thermostatting procedure, the resulting equations of motion are time-reversible. The observed macroscopic irreversibility is a consequence of the Lyapunov instability of the system measured by the spectrum of Lyapunov exponents. The phase-space distribution does not remain smooth and well-behaved but collapses onto a multifractal strange attractor in phase space with an information dimension smaller than the phase-space dimension. The attractor even remains fractal if it is projected onto a subspace spanned only by phase-space variables which are not directly affected by the computer thermostat. This is demonstrated for boundary-driven planar Couette flow, for which the number of variables associated with the thermostatted boundary can be made small.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. G. Hoover, Computational Statistical Mechanics, Studies in Modern Thermodynamics 11 (Elsevier, Amsterdam, 1991).
G. Ciccotti and W. G. Hoover (eds.), Molecular-Dynamics Simulation of Statistical - Mechanical Systems, Course XCVII of Proc. Int. School of Physics Enrico Fermi, Varenna, (North-Holland, Amsterdam, 1986).
M. P. Allen and D. J. Tildesley,Computer Simulations of Liquids(Clarendon Press, Oxford, 1987).
M. S. Green, J. Chem. Phys.20, 1281 (1952);22, 398 (1954).
R. Kubo, J. Phys. Soc. (Jpn.) 12, 570 (1957).
R. Zwanzig, Ann. Rev. Phys. Chem. 16, 67 (1965).
B. J. Alder and T. E. Wainwright, Phys. Rev. A 1, 18 (1970).
B. J. Alder and E. E. Alley, in Perspectives in Statistical Physics, edited by H. J. Raveche (Noth-Holland, Amsterdam, 1981), p. 3.
W. G. Hoover and W. T. Ashurst, Adv. Theor. Chemistry 1, 1, 1975.
D. J. Evans and G. P. Morriss,Statistical Mechanics of Nonequilibrium Liquids(Academic Press, London, 1990).
S. Y. Liem, D. Brown and J. H. R. Clarke, Phys. Rev. A 45, 3706 (1992).
B. Holian and D. J. Evans, J. Chem. Phys. 83, 3560 (1985).
D. J. Evans and G. P. Morriss, Molec. Phys. 64, 521 (1988).
W. T. Ashurst, Ph. D. Thesis, University of California at Davis, 1974.
B. L. Holian and D. J. Evans, J. Chem Phys., 78, 5147 (1983).
G. Ciccotti, G. Jacucci and I. R. McDonald, Phys. Rev A 13, 426 (1976)
J. Stat. Phys. 21, 1 (1979).
W. Loose and G. Ciccotti, Phys. Rev. A 45, 3859 (1992).
W. Loose and S. Hess, Physica A 174, 47 (1991).
A. Baranyai and D. J. Evans, Molec. Phys. 74, 353 (1991).
S. Nosé, Molec. Phys. 52, 255 (1984).
D. J. Evans, J. Chem. Phys. 78, 3297 (1983).
D. J. Evans, W. G. Hoover, B. H. Failor, B. Moran A. J. C. Ladd, Phys. Rev. A 28, 1016 (1983).
A. Sommerfeld, Vorlesungen über Theoretische Physik, Band 1: Mechanik, Akademische Verlagsgesellschaft, Leipzig, 1962.
S. Nosé, J. Chem. Phys. 81, 511 (1984).
W. G. Hoover, Phys. Rev. A 31, 1695 (1985).
H. A. Posch, W. G. Hoover and F. J. Vesely, Phys. Rev. A 33, 4253 (1986).
D. Kusnezov, A. Bulgac and W. Bauer, Annals of Physics 204, 155 (1990)
R. G. Winkler, Phys. Rev. A 45, 2250 (1992).
G. J. Martyna, M. L. Klein and M. Tuckerman, “Nosé-Hoover Chains: the Canonical Ensemble via Continuous Dynamics” (Preprint, 1992).
A. Bulgac and D. Kusnezov, Phys. Rev B 45, 1988 (1992).
H. A. Posch and W. G. Hoover, Phys. Rev. A 38, 473 (1988).
W. G. Hoover, Lecture Notes in Physics 132, Systems far from equilibrium, edited by: J. Ehlers et alii (Springer-Verlag, Berlin, 1980) p. 373.
W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst and B. Moran, Phys. Rev. A 22, 1690 (1980).
A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972).
D. J. Evans, Phys. Lett. A 91, 457 (1982)
Phys. Rev. A 34, 1449 (1986).
M. J. Gillan and M. Dixon, J. Phys. C 16, 869 (1983).
D. MacGowan D. J. Evans, Phys. Lett. A 117, 414 (1986).
W. Loose and S. Hess, Rheologica Acta 28, 91 (1989).
B. J. Ackerson, Physica A 174 15 (1991).
H. A. Posch and W. G. Hoover, Phys. Rev. A 39, 2175 (1989).
W. G. Hoover, H. A. Posch and C. G. Hoover, Chaos 2, 2 (1992).
H. A. Posch and W. G. Hoover, in preparation.
B. L. Holian, Phys. Rev. A 34, 4238 (1986).
W. G. Hoover, H. A. Posch, B. L. Holian, M. J. Gillan, M. Mareschal and C. Massobrio, Molec. Simulation 1, 79 (1997).
H. A. Posch, W. G. Hoover and B. L. Holian, Ber. Bunsenges. Phys. Chem. 94, 250 (1990).
W. G. Hoover and B. Moran, Phys. Rev. A 40, 5319 (1989).
G. P. Morriss, Phys. Lett A 143, 307 (1989)
Phys. Rev. A 39 4811 (1989).
J. D. Farmer, E. Ott and J. A. Yorke, Physica 7D, 153 (1983).
J. Mandelbrot, Fluid Mech., 62, 331 (1974).
U. Frisch and G. Parisi, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Research, edited by M. Ghil, R. Benzi and G. Parisi (North-Holland, Amsterdam, 1985) p.84.
T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A 33, 1141 (1986).
A. B. Chhabra and R. V. Jensen, Phys. Rev. Lett. 62, 1327 (1989).
J. Kaplan and J. Yorke, in Functional Differential Equations and the Approximation of Fixed Points, Vol. 730 of Lecture Notes in Mathematics, eds.: H. 0. Peitgen and H. 0. Walther (Springer-Verlag, Berlin, 1980).
R. Preston, The Mountains of Pi, The New Yorker, Mar. 2,1992, p. 36.
V. I. Arnold, Mathematical methods of classical mechanics(Springer, Berlin, 1989).
D. J. Evans, E. G. D. Cohen and G. P. Morriss, Phys. Rev. A 42, 5990 (1990).
B. L. Holian, W. G. Hoover and H. A. Posch, Phys. Rev. Lett.59, 10 (1987).
J. L. Lebowitz, first round-table remarks inSimulation of Complex Hydrodynamic Phenomena, edited by M. Mareschal, NATO-ASI in Alghero, Sardinia (Plenum, New York, 1992).
S. Goldstein, C. Kipnis and N. Ianiro, J. Stat. Phys.41, 915 (1985).
S. Goldstein, J. L. Lebowitz and E. Presutti, Colloquia Math. Soc. Janos Bolyai27, Random fields (Esztergom, Hungary, 1981).
E. T. Jaynes, Papers on Probability, Statistics and Statistical Physics, edited by R. D. Rosenkrantz (Kluwer, Dordrecht, 1989).
D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, (Consultants bureau, New York, 1974).
W. G. Hoover, J. Stat. Phys. 42, 587 (1986).
H. A. Posch, H. Narnhofer and W. Thirring, J. Stat. Phys.65, 555 (1991).
W. Pusz and S. L. Woronowicz, Commun. Math. Phys.58, 273 (1978).
A. Lenard, J. Stat. Phys.19, 575 (1978).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Posch, H.A., Hoover, W.G. (1992). Nonequilibrium Molecular Dynamics of Classical Fluids. In: Teixeira-Dias, J.J.C. (eds) Molecular Liquids: New Perspectives in Physics and Chemistry. NATO ASI Series, vol 379. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2832-2_30
Download citation
DOI: https://doi.org/10.1007/978-94-011-2832-2_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5258-0
Online ISBN: 978-94-011-2832-2
eBook Packages: Springer Book Archive