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a paradox of decreasing entropy in multiscale monte carlo grain growth simulations一个悖论多尺度熵减少的蒙特卡罗模拟晶粒生长
Entropy 2008, 10, 49-54; DOI: 10.3390/entropy-
OPEN ACCESS
entropy
ISSN 1099-4300
/entropy
Short Note
A Paradox of Decreasing Entropy in Multiscale Monte Carlo
Grain Growth Simulations
Michael Nosonovsky * and Sven K. Esche
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA
* Author to whom correspondence should be addressed; E-mail: Nosonovsky@
Received: 20 March 2008; in revised form: 9 June 2008 / Accepted: 14 June 2008 /
Published: 16 June 2008
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.
The entropy as a measure of
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