# ADVANCES IN CHEMICAL PHYSICS VOLUME 6 by I. PRIGOGINE

By I. PRIGOGINE

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For a classical mechanical system off degrees of freedom we may define a y phase space. This is a Euclidian space of 2f dimensions, one for each configuration coordinate (configuration space) q l . , . q,, and one for each momentum coordinate (momen- tum space) PI . 9,. The state of each system in the ensemble would be given by a “representative point” in the y phase space. The state of the ensemble as a whole would then be a “cloud of points” in the y phase space. We may also define a p phase space as that of one molecule in the system.

125), and the further simplification that Vjj- and q(j) are deemed to be only slowly varying within the subset, one derives The limits of integration may be extended to -a and +a because the value of the integral comes primarily from the region E , Ein, presumably, even for the "short" times to which we * See Reference 4 for a philosophic discussion of such an interaction potential in relation to practical problems in chemical kinetics. , t> h/AE. Evaluation of the definite integral yields Iw (127) with the result that as a first approximation w is independent of the time.

178), but note that Eq. (187) must be solved to apply this method. D. 66 They propose a technique wherein the equation is solved numerically for a wave packet representing the initial reactants. The spread of this wave packet into a product region of space determines the reaction probability. Because their primary purpose is to demonstrate the method, Mazur and Rubin make rather vigorous simplifications in their model, which is related to the colinear case of the reaction in Eq. (163). For a linear system of three atoms undergoing a reaction, A + BC+AC +B Eq.