THE GAUSSIAN THERMOSTAT, PHASE-SPACE COMPRESSION AND THE CONJUGATE PAIRING RULE

We recently proposed a possible variational principle for ergodic, non-equilibrium steady states (NESS) far from equilibrium (1991, Phys. Rev. Lett., 67, 2597). We provided computer simulation results in support of the hypothesis that in NESS with fixed internal energy, volume, number of particles and applied external field, the decrease of the volume of phase space which is accessible to the system is a local minimum with respect to variations in endogenous variables. This hypothesis is a microscopic and nonlinear generalization of the principle of minimum entropy production which is valid only for NESS close to equilibrium where both the local thermodynamic equilibrium and the Onsager reciprocal relations are valid. In the present paper, we point out that for a wide class of possible thermostatting mechanisms, the Gaussian thermostat minimizes the phase space compression. With respect to our variational principle, the Gaussian thermostat is therefore the optimal thermostat. Further, for this class of possible thermostats, the Gaussian thermostat is the only one which satisfies the recently discovered conjugate pairing rule.