{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:23:51Z","timestamp":1762176231759,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2008,6,16]],"date-time":"2008-06-16T00:00:00Z","timestamp":1213574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Grain growth in metals is driven by random thermal fluctuations and increases the orderliness of the system. This random process is usually simulated by the Monte Carlo (MC) method and Cellular Automata (CA). The increasing orderliness results in an entropy decrease, thus leading to a paradoxical apparent violation of the second law of thermodynamics. In this paper, it is shown that treating the system as a multiscale system resolves this paradox. MC\/CA simulations usually take into consideration only the mesoscale entropy. Therefore, the information entropy of the system decreases, leading to an apparent paradox. However, in the physical system, the entropy is produced at the nanoscale while it is consumed at the mesoscale, so that the net entropy is growing.<\/jats:p>","DOI":"10.3390\/entropy-e10020049","type":"journal-article","created":{"date-parts":[[2008,6,16]],"date-time":"2008-06-16T03:01:29Z","timestamp":1213585289000},"page":"49-54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations"],"prefix":"10.3390","volume":"10","author":[{"given":"Michael","family":"Nosonovsky","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA"}]},{"given":"Sven K.","family":"Esche","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA"}]}],"member":"1968","published-online":{"date-parts":[[2008,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/e1010001","article-title":"Diversity and Entropy","volume":"1","author":"Lin","year":"1999","journal-title":"Entropy"},{"doi-asserted-by":"crossref","unstructured":"Nosonovsky, M., Zhang, X., and Esche, S. K. (2008). Scaling of Monte Carlo simulations of grain growth in metals. Comput. Mater. Sci., (submitted).","key":"ref_2","DOI":"10.1088\/0965-0393\/17\/2\/025004"},{"doi-asserted-by":"crossref","unstructured":"Humphreys, F. J., and Hatherly, M. (1995). Recrystallization and Related Annealing Phenomena, Pergamon.","key":"ref_3","DOI":"10.1016\/B978-0-08-041884-1.50017-9"},{"unstructured":"Yu, Q., Nosonovsky, M., and Esche, S. K. (2008). On the accuracy of Monte Carlo Potts models for grain growth. J. Comp. Meth. Sci. 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Mag. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.mser.2007.09.001","article-title":"Multiscale friction mechanisms and hierarchical surfaces in nano- and bio-tribology","volume":"58","author":"Nosonovsky","year":"2007","journal-title":"Mater. Sci. Eng. R"},{"doi-asserted-by":"crossref","unstructured":"Nosonovsky, M., and Bhushan, B. (2008). Multiscale Dissipative Mechanisms and Hierarchical Surfaces: Friction, Superhydrophobicity, and Biomimetics, Springer Verlag. (in press).","key":"ref_13","DOI":"10.1007\/978-3-540-78425-8"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/2\/49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:20:50Z","timestamp":1760221250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/2\/49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6,16]]},"references-count":13,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2008,6]]}},"alternative-id":["e10020049"],"URL":"https:\/\/doi.org\/10.3390\/entropy-e10020049","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2008,6,16]]}}}