Intermediate Operators and the Kinetic Theory of Gases

A decreasing set of intermediate operators, L(N), are defined that are greater than the linearized Boltzmann operator in the sense that they correspond to collision models with a lower rate of entropy production. With these operators upper bounds for transport properties may be calculated to supplement the lower bounds calculated by the usual variation method. Two examples are given, both for the rigid-sphere model. One is the thermal conductivity, and the other, the perturbation to the reaction rate by the depletion of the faster moving molecules. In the second instance, new lower bounds are calculated as well. The extension to other collision models is indicated. We also find that a measured transport property determines a mean relaxation frequency that must lie within the spectrum of relaxation frequencies of the fluctuation variable corresponding to the flux.