C Richard et al 1998 J. Phys. A: Math. Gen. 31 6385 doi:10.1088/0305-4470/31/30/007
C Richard, M Höffe, J Hermisson and M Baake
Show affiliationsWe introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
82B30 Statistical thermodynamics (See also 80-XX)
Issue 30 (31 July 1998)
Received 5 January 1998
C Richard et al 1998 J. Phys. A: Math. Gen. 31 6385
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