The phasonic specific heat contributions of the octagonal Ammann-Beenker tiling, the Tubingen triangle tiling and the 60°-rhombus tiling are calculated by random-izing the tilings via elementary flips. Using a Monte Carlo simulation we compare different energy models and estimate the typical shapes of the phasonic specific heat and of the entropies of the tilings. The same algorithm is used to calculate the self-diffusion properties of the Ammann-Beenker tiling. We find a tempera-ture dependent correction to the ordinary vacancy diffusion of simple crystals and comment on possible implications on real quasicrystals.
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