Advances in Chemical Physics, Volume 135 (Special Volume in - download pdf or read online

By Stuart A. Rice

ISBN-10: 0470121904

ISBN-13: 9780470121900

ISBN-10: 0471682330

ISBN-13: 9780471682332

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The duration of a collision). In what way could one get rid of the restriction to small values of the characteristic parameter and generalize this behavior to systems with arbitrarily strong coupling? A first answer to this difficult question was elaborated from 1966 on. A new methodology was introduced by C. George in 1967. It consisted of identifying a ‘‘piece’’ of of the distribution function that would evolve irreversibly to equilibrium, following a ‘‘subdynamics,’’ independently of its complementary part.

It provided, in the first place, a very general basic formalism, which turned out to be a very fruitful working tool. As stressed above, it gave rise to a flowering of results of enormous diversity. It is true that other groups (such as the Russian school initiated by N. N. Bogoliubov, and the Dutch school directed by G. Uhlenbeck) worked independently in the same direction; the results always turned out to be equivalent. Prigogine was always in the forefront: A proof is the large number of foreign visitors, co-workers, and students he attracted.

In the deterministic case the value of the distribution function at time t depends on its value at a single point of the trajectory (initial condition); the latter point may be taken indifferently in the past or in the future of the time t. In the stochastic case, the value of e r at a time t > 0 depends on the values taken by e r at a time t0 ¼ 0 in all points of phase space; this is clearly expressed by the integral in Eq. (12). Indeed, every point o0 has a nonzero probability of arriving in o at time t.

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Advances in Chemical Physics, Volume 135 (Special Volume in Memory of Ilya Prigonine) by Stuart A. Rice


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