Differential‐Operator Approximations to the Linear Boltzmann Equation

Armand Siegel
1960 Journal of Mathematical Physics  
A measure of deviation from equilibrium of an ensemble of particles is proposed, which is physically appropriate and of especially simple form when expressed in terms of the expansion coefficients of the ensemble distribution function with respect to the system of orthogonal polynomials obtained by using the equilibrium distribution function as weight function. The linear Boltzmann operator can then be expanded in a series of terms which, under certain circumstances, may be regarded as of
more » ... egarded as of successively diminishing magnitude in their effect on the rate of approach to equilibrium. This expansion of the operator is different from the expansion due to Kramers (later discussed by Moyal) in derivate moments, commonly used in approximate stochastic treatments of irreversible processes. With the aid of a *
doi:10.1063/1.1703668 fatcat:66vjj2qjjvf6togokzoqvi4lim