By Stuart A Rice; I Prigogine
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Extra resources for Advances in Chemical Physics [Vol 15]
On any particular occasion, 0, the microscopic motion gives the variables X, X’, and the corresponding momenta, as functions of the time t ; for example we may have X’ = G(t). This function G ( t ) describes part of the history of what occurred on the occasion 0. We could reconstruct more of this history by studying the system within V on the basis of the 43 RELAXED MOTION Hamiltonian 5j =H + W ( X ,G(t),t ) = H + w(X,t ) In fact, with the same initial data, the same solution will be obtained as in 0.
6 The passage from these to (p, u,, R ) , which are functions of (x) on V” (as well as o f t ) is as follows: From the additivity of the random variables M(d),P ( d ) , E ( d ) follows that of their expected values (with respect to 9). and a-additive). c), p(x)u,(x), p(x)E(x). This identification is the matheinatically exact rendering of the conventional physical-pictorial reasoning. An identical line of reasoning leads from our additive invariants to certain important macroscopic fluxes. Here, instead of considering a fixed epoch f and a three-dimensional spacial region in Y ,we consider a surface Y in, or on the boundary of, Y ,and interval of time 9-.
But on an even less cosmological scale there is a deep difficulty involved with such an approach and that is to make a distinction between what is truly asymptotic (stable particles) and only approximately asymptotic (unstable particles). Such a theory needs at least an independent check and this is one of the aims of the approach I shall describe in the next paragraphs. We may now make the direction in which we intend to go more precise. All problems related to decaying atomic states or unstable particles involve interacting fields (or atoms and fields).
Advances in Chemical Physics [Vol 15] by Stuart A Rice; I Prigogine