Advances in Chemical Physics, Volume 135: Special Volume in by Stuart A. Rice

By Stuart A. Rice

This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each zone of the self-discipline. This stand-alone certain issues quantity studies fresh advances in electron-transfer study with major, up to date chapters through across the world well-known researchers.

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Extra info for Advances in Chemical Physics, Volume 135: Special Volume in Memory of Ilya Prigogine (Volume v)

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This work (actually very difficult to read, and using a very heavy formalism) had the effect of a bomb in Brussels. Prigogine associated himself with Robert Brout (who was at that time a postdoc in Brussels) in order to understand, deepen, and develop Van Hove’s ideas. 8 Although still influenced by Van Hove’s paper, this work by Brout and Prigogine is a generalization of the latter, as well as a simpler and more transparent presentation. 7 As a trivial example, think of the exponential function expðÀtÞ for positive times: Its series expansion contains all positive powers of time, t; t2 ; t3 ; .

Thus, in order to satisfy condition (iv), the transformation à must be noncanonical. Condition (v) raises a subtle problem. If it were satisfied, we would be tempted to say that the transformation r ! Ãr involves ‘‘no loss of memory’’ (as stated by MPC), because we could always reverse it. In order, however, to have a ‘‘complete equivalence’’ between the two representations, it is necessary that, upon reversion of the transformation we find again a true distribution function r. This implies, in particular, the preservation of positivity: ÃÀ1 ðÃrÞ !

Html ilya prigogine: his life, his work 29 They would become the ‘‘stars’’ of Prigoginian statistical mechanics. Their importance lies in the fact that, whenever it is possible to determine these variables by a canonical transformation of the initial phase space variables, one obtains a description with the following properties. The action variables Jn ðn ¼ 1; 2; . . ; N, where N is the number of degrees of freedom of the system) are invariants of motion, whereas the angles an increase linearly in time, with frequencies on ðJÞ, generally action-dependent.

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