Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

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Abstract:

We investigate a piecewise linear (area-preserving) map T describing two coupled baker transformations on two squares, with coupling parameter 0≤c≤1. The resulting dynamical system is Kolmogorov for any c≠0. For rational values of c, we construct a generating partition on which T induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given for c=2-n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed. © 1985 Plenum Publishing Corporation.