Monte Carlo simulations including energy from an entropic force

Several experimental techniques have shown that the primary response of many materials comes from a heterogeneous distribution of independently relaxing nanoscale regions; but most Monte Carlo simulations have homogeneous correlations. Resolving this discrepancy may require including the energy need...

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Bibliographic Details
Published in:Physica A 2012-11, Vol.391 (22), p.5384-5391
Main Author: Chamberlin, Ralph V.
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Conservation
Correlation
Entropic force
Entropy
Heterogeneous dynamics
Ising model
Monte Carlo methods
Monte Carlo simulations
Nanostructure
Nonlinearity
Small-system thermodynamics
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Summary:Several experimental techniques have shown that the primary response of many materials comes from a heterogeneous distribution of independently relaxing nanoscale regions; but most Monte Carlo simulations have homogeneous correlations. Resolving this discrepancy may require including the energy needed to change the configurational entropy, which is often used in theoretical treatments of thermal fluctuations, but not in computer simulations. Here the local configurational entropy is shown to give a nonlinear correction to the Metropolis algorithm that restores conservation of energy, maintains maximum entropy, and yields heterogeneous correlations. The nonlinear correction also improves agreement between Monte Carlo simulations of the Ising model and measurements of specific heat and structural correlations from the Jahn–Teller distortion in LaMnO3. ► A correction from configurational entropy is added to the Metropolis algorithm. ► The correction allows Monte Carlo simulations to exhibit extensive entropy. ► Maximum entropy is maintained during normal thermal fluctuations. ► Conservation of energy includes work done against an entropic force. ► Improved agreement is found between the Ising model and measurements of LaMnO3.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2012.06.016