Non-linear reciprocity in extended thermodynamics from the Robertson formalism

Robertson has found a projection operator which, applied to the Liouville equation, yields an exact equation for , the information-theoretic phase-space distribution. If the Robertson equation is multiplied by a set [0pt]{} of functions representing physical fluxes, odd under momentum reversal and even under configuration inversion, a set of evolution equations is obtained for time-dependent ensemble averages which are variables of extended thermodynamics. In earlier work, a perturbation calculation was developed, assuming just one variable , for an operator [0pt] occurring in the Robertson equation. This calculation is extended here to the case where there are variables. The coefficients in the evolution equations depend on {} and explicitly on time t at short times. It is shown here that these coefficients exhibit Onsager symmetry at long times, after the transient explicit t-dependence has disappeared, to . Received 13 September 1999 and Received in final form 4 April 2000