Advances in Chemical Physics [Vol 15] by Stuart A Rice; I Prigogine

By Stuart A Rice; I Prigogine

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61 . . 62 . 1. THE BASIC ENIGMA As has long been known, every derivation of the bulk properties of matter from its atomic properties by statistical methods encounters essential difficulties of principle. , equilibrium) the development does not take the form of a deductive science. , Newtonian or relativistic mechanics, electromagnetism, quantum theory, etc. The present paper, after focusing on this difficulty, seeks a way out by exploring the properties of a special class of statistical kinetics to be called “ relaxed motion ” and to be defined by methods of generalized information theory.

FJ. F, uniquely, So’ would then imply S,, and the sun1 on the right in Eq. (2) would reduce to its fir5t term. On the basis of these ideas, we are led to the study of relaxed motion, according to the following: B. KOOPMAN 48 DEFINITION : Under the conditions set forth above regarding the existence of the relaxation time 7 , a tangential macroscopic path (Eq. (2))shall be said to constitute a mode of z-relaxed motion initiating at (p, u,, E ) i f P a p , Q, of Eq. (1) minimize the I(SoS,) given by Eq.

36) by 9. Once the initial state is chosen such as to satisfy Eq. ” Similarly if at some initial time (which may be taken in the remote past) the particle description 6 was valid, it will be valid for all times later. To insure the validity at the initial time it would be sufficient to assume that then the system was formed by stable particles only. It is interesting that two widely different questions such as the validity of the kinetic (or thermodynamic) description of many-body systems and the particle description may be related to self-propagating initial correlations.

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