Quantum statistics are also recreated in Maximal Entropy Random Walk, which has lots of known applications:
"MERW is used in various fields of science. A direct application is choosing probabilities to maximize transmission rate through a constrained channel, analogously to Fibonacci coding. Its properties also made it useful for example in analysis of complex networks(1), like link prediction, community detection and centrality measures. Also in image analysis, for example for detecting visual saliency regions, object localization, tampering detection, or tractography problem.
Additionally, it recreates some properties of quantum mechanics, suggesting a way to repair the discrepancy between diffusion models and quantum predictions, like Anderson localization.
(1) R. Sinatra, J. Gómez-Gardenes, R. Lambiotte, V. Nicosia, Maximal-entropy random walks in complex networks with limited information, Phys. Rev. E, 2011.
 R.H. Li, J.X. Yu, J. Liu, Link Prediction: the Power of Maximal Entropy Random Walk, CIKM '11, 2011.
 J. Ochab, Z. Burda, Maximal entropy random walk in community detection, Z. Eur. Phys. J., 2013.
 J.C. Delvenne, A.S. Libert, Centrality measures and thermodynamic formalism for complex networks, Phys. Rev. E, 2011.
 J.G. Yu, J. Zhao, J. Tian, Y. Tan, Maximal entropy random walk for region-based visual saliency, IEEE Transactions on Cybernetics, 2014.
 L. Wang, J. Zhao, X. Hu, J. Lu, Weakly supervised object localization via maximal entropy random walk, ICIP, 2014.
 P. Korus, J. Huang, Improved Tampering Localization in Digital Image Forensics Based on Maximal Entropy Random Walk, IEEE Signal Processing Letters, 2016.
 V.L. Galinsky, L.R. Frank, Simultaneous multi-scale diffusion estimation and tractography guided by entropy spectrum pathways, IEEE Transactions on Medical Imaging, 2015.
 Z. Burda, J. Duda, J. M. Luck, and B. Waclaw, Localization of the Maximal Entropy Random Walk, Phys. Rev. Lett., 2009.