By Stuart A. Rice
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Extra resources for Advances in Chemical Physics, Volume 135 (Special Volume in Memory of Ilya Prigonine)
Physically, this implies that two trajectories, arbitrarily close together at a certain (initial) time, end up diverging exponentially from each other after a long time (this property is related to ‘‘deterministic chaos‘‘). There exist various degrees of instability. MPC prove (with full mathematical rigor) that the ‘‘mixing’’ condition is necessary for the existence of Ã (we do not discuss here the details of the deﬁnitions). MGC showed later that a somewhat stronger condition (K-ﬂows = Kolmogorov ﬂows) is sufﬁcient.
In their 1973 paper, PGHR performed a synthesis of the projector method of C. George and the idea of a transformation of r. The PGHR paper was considered for several years as the ‘‘bible’’ of Prigogine’s group. The 10 A signiﬁcant anecdote: During a summer school in Sitges, Spain, in 1972, an anonymous student replaced the lettering of the announcement of a lecture by Rosenfeld about Prigoginian statistical mechanics by substituting the anagram: ‘‘EL DEFENSOR’’! ilya prigogine: his life, his work 19 authors developed a theory leading to a ‘‘causal irreversible dynamics’’ and to a deﬁnition of entropy.
Prigogine, Contribution a` la thermodynamique de la matie`re dans un champ e´lectromagne´tique (Contribution to thermodynamics of matter in an electromagnetic ﬁeld), Me´moires Acad. Roy. , Cl. Sciences, 28. 6. I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Charles C Thomas Publishers, Springﬁeld, IL, 1955. , 1967. Translations in Russian, Serbo-Croatian, French, Italian, and Spanish. 7. I. Prigogine (with the collaboration of V. Mathot and A. Bellemans), The Molecular Theory of Solutions, North Holland Publishers, Amsterdam, 1957.
Advances in Chemical Physics, Volume 135 (Special Volume in Memory of Ilya Prigonine) by Stuart A. Rice