Lyapunov exponent pairing for a thermostatted hard-sphere gas under shear in the thermodynamic limit.

Abstract

We demonstrate why for a sheared gas of hard spheres, described by the SLLOD equations with an isokinetic Gaussian thermostat in between collisions, deviations of the conjugate pairing rule for the Lyapunov spectrum are to be expected, employing a previous result that for a large number of particles N, the isokinetic Gaussian thermostat is equivalent to a constant friction thermostat, up to 1/sqrt[N] fluctuations. We also show that these deviations are at most of the order of the fourth power in the shear rate.