We demonstrate why for a sheared gas of hard spheres, described by the SLLOD equations with an iso-kinetic 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 iso-kinetic 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.
Categories: nlin.CD cond-mat.stat-mech