Abstract
The symmetry of the spectrum of Lyapunov exponents provides a useful quantitative connection between properties of dynamical systems consisting ofN interacting particles coupled to a thermostat, and nonequilibrium statistical mechanics. We obtain here sufficient conditions for this symmetry and analyze the structure of 1/N corrections ignored in previous studies. The relation of the Lyapunov spectrum symmetry with some other symmetries of dynamical systems is discussed.
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References
G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn,Meccanica 15:9 (1980).
I. Goldhirsch, P. L. Sulem, and S. A. Orszag,Physica D 27:311 (1987).
V. I. Arnold,Mathematical Methods in Classical Mechanics (Springer-Verlag, Berlin, 1978).
U. Dressler,Phys. Rev. A 38:2103 (1988).
W. G. Hoover and H. A. Posch,Phys. Lett. A 123:227 (1987).
H. A. Posch and W. G. Hoover,Phys. Rev. A 39:2175 (1989).
D. J. Evans, E. G. D. Cohen, and G. P. Morris,Phys. Rev. A 42:5990 (1990).
S. Sarman, D. J. Evans, and G. P. Morris,Phys. Rev. A 45:2233 (1992).
G. P. Morris,Phys. Rev. A 37:2118 (1988).
J. P. Eckman and D. Ruelle,Rev. Mod. Phys. 57:617 (1985).
W.-H. Steeb and A. Kunick,Phys. Rev. A 25:2889 (1982).
D. Gupalo, inNEEDS'92 Proceedings, V. G. Makhankov and O. K. Pashaev, eds. (World Scientific, Singapore, 1993).
D. J. Evans and G. P. Morris,Statistical Mechanics of NonEquilibrium Liquids (Academic Press, London, 1990).
L. A. Pars,A Treatise on Analytical Dynamics (Oxbow Press, Woodbridge, Connecticut, 1979).
Ju. I. Naimark and N. A. Fufaev,Dynamics of Nonholonomic Systems (AMS, Providence, Rhode Island, 1972).
A. Baranyai, D. J. Evans, and E. G. D. Cohen,J. Stat. Phys. 70:1085 (1993).
J. A. G. Roberts and G. R. W. Quispel,Phys. Rep. 216:63 (1992).
A. S. Kaganovich and D. Gupalo, Time-reversibility, ergodicity and Lyapunov exponents in thermostatted systems, preprint, Rockefeller University (1993).
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Gupalo, D., Kaganovich, A.S. & Cohen, E.G.D. Symmetry of Lyapunov spectrum. J Stat Phys 74, 1145–1159 (1994). https://doi.org/10.1007/BF02188220
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DOI: https://doi.org/10.1007/BF02188220