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 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/N fluctuations. We also show that these deviations are at most of the order of the fourth power in the shear rate.
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