By Stuart A. Rice
Read Online or Download Advances in Chemical Physics, Volume 135 (Special Volume in Memory of Ilya Prigonine) PDF
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Extra info for Advances in Chemical Physics, Volume 135 (Special Volume in Memory of Ilya Prigonine)
This is a crucial question for establishing the molecular basis of thermodynamics. It was stated, and solved in the special case of dilute gases, by Ludwig Boltzmann in 1872. But this solution required a partial abandonment of the laws of mechanics, along with entering into the game of probabilities. , the majority of the physicists of that time). ’’: Boltzmann’s theory led later to a determination of the macroscopic transport coefﬁcients of gases with a great precision, and it was fully supported by experiment.
These transformations conserve the positivity of the distribution functions (that must, at every time, represent a probability density) and admit the equilibrium distirbution as a stationary solution: y rðoÞ ! 0; ðaÞ e rðoÞ ! 0 ! Wt e y req ¼ e ðbÞ Wt e req for t>0 MPC restrict themselves, moreover, to monotonous Markov processes: y ðbÞ k Wt ðe rÀe req Þ k! 1 The authors then ask the following question: Do there exist deterministic dynamical systems that are, in a precise sense, ‘‘equivalent’’ to a monotonous Markov process?
It became an extraordinary best-seller, translated into numerous languages. The book is, however, not easy to read. It is directed, in principle, to a wide, ‘‘enlightened,’’ but not specialized, audience. But, a reader of ‘‘literary type’’ would not grasp the more technical aspects, often suggested rather than explained, whereas a ‘‘scientiﬁc-type’’ reader would probably be hindered by the philosophical erudition. Prigogine exposes here his vision of the world, which he presents as a new dialogue between Science and Philosophy, made possible by his conception of time.