Kinetic approach to the Gaussian thermostat in a dilute sheared gas in the thermodynamic limit.

A dilute gas of particles with short range interactions is considered in a shearing stationary state. A Gaussian thermostat keeps the total kinetic energy constant. For infinitely many particles it is shown that the thermostat becomes a friction force with constant friction coefficient. For finite number of particles N, the fluctuations around this constant are of order 1/squareroot[N], and distributed approximately Gaussian with deviations for large fluctuations. These deviations prohibit a derivation of fluctuation-dissipation relations far from equilibrium, based on the fluctuation theorem.