 98165 F. Bonetto, E.G.D. Cohen, C. Pugh
 On the Validity of the Conjugate Pairing Rule for Lyapunov Exponents
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Mar 9, 98

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Abstract. For Hamiltonian systems subject to an external potential, which in the
presence of a thermostat will reach a nonequilibrium stationary state,
Dettmann and Morriss proved a strong conjugate pairing rule (SCPR) for
pairs of Lyapunov exponents in the case of isokinetic (IK) stationary
states which have a given kinetic energy. This SCPR holds for all
initial phases of the system, all times t and all numbers of particles
N. This proof was generalized by Wojtkovski and Liverani to include
hard interparticle potentials. A geometrical reformulation of those
results is presented. The present paper proves numerically, using
periodic orbits for the Lorentz gas, that SCPR cannot hold for
isoenergetic (IE) stationary states, which have a given total internal
energy. In that case strong evidence is obtained for CPR to hold for
large N and t, where it can be conjectured that the larger N, the
smaller t will be. This suffices for statistical mechanics.
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