ε-Machine spectral reconstruction theory: A direct method for inferring planar disorder and structure from X-ray diffraction studies Dowman P. Varn Complexity Sciences Center & Physics Department, University of California, Davis Santa Fe Institute Department of Physics and Astromony, University of Tennessee, Knoxville Geoffrey S. Canright Telenor Research and Development Department of Physics and Astronomy, University of Tennessee, Knoxville James P. Crutchfield Complexity Sciences Center & Physics Department, University of California, Davis Santa Fe Institute Abstract: In previous publications [Varn et al. (2002). Phys. Rev. B, 66, 174110; Varn et al. (2007). Acta Cryst. B63, 169-182] we introduced and applied a new technique for discovering and describing planar disorder in close-packed structures directly from their diffraction patterns. Here, we provide the theoretical development behind those results, adapting computational mechanics to describe one- dimensional structure in materials. We show that the resulting statistical model of the stacking structure--called the ε-machine--allows the calculation of measures of memory, structural complexity and configurational entropy. The methods developed here can be adapted to a wide range of experimental systems in which power spectra data are available. A copy of this paper in pdf format: ε-Machine spectral reconstruction theory: A direct method for inferring planar disorder and structure from X-ray diffraction studies Citation: D.P. Varn, G. S. Canright and J.P. Crutchfield, Acta Crystallogr., Sec A: 69 (2013) 197-206. Referee Reports