Abstract
We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0⩽c⩽1. The resulting dynamical system is Kolmogorov for anyc≠0. For rational values ofc, we construct a generating partition on whichT 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 forc=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.
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Elskens, Y., Kapral, R. Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction. J Stat Phys 38, 1027–1049 (1985). https://doi.org/10.1007/BF01010428
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DOI: https://doi.org/10.1007/BF01010428