1. Crystallography
• D. P. Varn and J. P. Crutchfield, "From Finite to Infinite Range Order via Annealing: The Causal Architecture of Deformation Faulting in Annealed Close-Packed Crystals". Santa Fe Institute Working Paper 03-07-045.
  [Abstract] [ps.gz] [ps] [pdf]
  arXiv.org/abs/cond-mat/0307296.
• D. P. Varn, G. S. Canright, and J. P. Crutchfield, "Discovering Planar Disorder in Close-Packed Structures from X-Ray Diffraction: Beyond the Fault Model", Santa Fe Institute Working Paper 02-03-014.
  [Abstract] [ps.gz]  [ps] [pdf]
  arXiv.org/abs/cond-mat/0203290.
2. Dripping faucet
• W. M. Gonçalves and R. D. Pinto and J. C. Sartorelli and M. J. de Oliveira, "Inferring Statistical Complexity in the Dripping Faucet Experiment", Physica A 257 (1998) 385-389.
3. Atmospheric turbulence
• A. J. Palmer and C. W. Fairall and W. A. Brewer, "Complexity in the Atmosphere", IEEE Trans. Geosci. Remote Sens. 38 (2000) 2056-2063.
4. Geomagnetic data
• Richard W. Clarke, Mervyn P. Freeman and Nicholas W. Watkins, "The Application of Computational Mechanics to the Analysis of Geomagnetic Data", Phys. Rev. E 67 (2003) 160-203.
5. Molecular systems
• D. Nerukh, G. Karvounis and R. C. Glen, "Complexity of classical dynamics of molecular systems. I. Methodology", J. Chem. Phys. 117 (2002) 9611-9617.
• D. Nerukh, G. Karvounis and R. C. Glen, "Complexity of classical dynamics of molecular systems. II. Finite Statistical complexity of water-Na⁺ system", J. Chem. Phys. 117 (2002) 9618-9622.

Computational mechanics has also been used to analyze structural complexity in a number of nonlinear processes:

1. Cellular Automata
• J. E. Hanson and J. P. Crutchfield, "Computational Mechanics of Cellular Automata: An Example", Physica D 103 (1997) 169--189.
  [Abstract] [ps.gz]
  Santa Fe Institute Working Paper 95-10-95.
2. One-dimensional maps
• J. P. Crutchfield and K. Young, "Inferring Statistical Complexity", Physical Review Letters 63 (1989) 105-108.
  [Abstract] [zipped pdf] [pdf]
• J. P. Crutchfield and K. Young, "Computation at the Onset of Chaos", in Entropy, Complexity, and Physics of Information, W. Zurek, editor, SFI Studies in the Sciences of Complexity, VIII, Addison-Wesley, Reading, Massachusetts (1990) 223-269.
  [Abstract] [ps.gz] [ps] [pdf]
3. One-dimensional Ising model
• David Polant Feldman, "Computational Mechanics of Classical Spin Systems", Ph.D. Thesis, University of California, Davis (1998).
• J. P. Crutchfield and D. P. Feldman, "Statistical Complexity of Simple 1D Spin Systems", Physical Review E 55:2 (1997) 1239R-1243R.
  [Abstract] [ps.gz]
4. Two-dimensional Ising model
• D. P. Feldman and J. P. Crutchfield, "Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy", Physical Review E 67 (2003) 051104.
  [Abstract] [pdf] [ps] [ps.gz]
  Santa Fe Institute Working Paper 02-12-065. arXiv.org/abs/cond-mat/0212078.
5. Hidden Markov Models
• D. R. Upper, "Theory and Algorithms for Hidden Markov Models and Generalized Hidden Markov Models", Ph.D. Dissertation, Mathematics Department, University of California (February 1997).
  [Abstract] [ps.gz] [gzipped pdf]