Stefano Siboni, "About the existence of the thermodynamic limit for some deterministic sequences of the unit circle", International Journal of Mathematics and Mathematical Sciences, vol. 24, Article ID 489573, 7 pages, 2000. https://doi.org/10.1155/S0161171200004282
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle
We show that in the set , endowed with the usual Lebesgue measure, for almost all the limit exists and is equal to zero. The result is related to a characterization of relaxation to equilibrium in mixing automorphisms of the two-torus. It is nothing but a curiosity, but maybe you will find it nice.
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