The concept of distributive process, recently developed as a description of systems which evolve through ‘random’ energy-transfer in binary collision complexes4) is here extended to the case of energy quanta exchanged similarly between discrete, degenerate internal energy-levels. A corresponding exact solution of the Master Equation is forthcoming, in which the eigenvectors are now orthogonal polynomials of the discrete variable, viz. the Meixner and Hahn types. The relaxation times of the discrete models prove to be identical with those of their continuous counterparts and the autocorrelation functions for equilibrium fluctuations are likewise of strictly exponential type. All results tend naturally to their continuous analogues as the quantity (hv/kBT) for the heat-bath tends to zero.
