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Entropy 2008, 10(2), 49-54; doi:10.3390/entropy-e10020049
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A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations

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Received: 20 March 2008; in revised form: 9 June 2008 / Accepted: 14 June 2008 / Published: 16 June 2008
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Abstract: 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.
Keywords: grain growth; Monte Carlo simulation; Cellular Automata; multiscale modeling. grain growth; Monte Carlo simulation; Cellular Automata; multiscale modeling.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Nosonovsky, M.; Esche, S.K. A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations. Entropy 2008, 10, 49-54.

AMA Style

Nosonovsky M, Esche SK. A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations. Entropy. 2008; 10(2):49-54.

Chicago/Turabian Style

Nosonovsky, Michael; Esche, Sven K. 2008. "A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations." Entropy 10, no. 2: 49-54.


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