On the Validity of the Conjugate Pairing Rule for Lyapunov Exponents
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
30 pages, 33 ps figure
30 pages, 33 ps figure