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Finite-Temperature Coarse-Graining of One-Dimensional Models: Mathematical Analysis and Computational Approaches

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Abstract

We present a possible approach for the computation of free energies and ensemble averages of one-dimensional coarse-grained models in materials science. The approach is based upon a thermodynamic limit process, and makes use of ergodic theorems and large deviations theory. In addition to providing a possible efficient computational strategy for ensemble averages, the approach allows for assessing the accuracy of approximations commonly used in practice.

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Authors and Affiliations

  1. Laboratoire J.-L. Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252, Paris Cedex 05, France

    X. Blanc

  2. CERMICS, École Nationale des Ponts et Chaussées, Université Paris-Est, 6 et 8 avenue Blaise Pascal, 77455, Marne-La-Vallée Cedex 2, France

    C. Le Bris

  3. Institut Navier, LAMI, École Nationale des Ponts et Chaussées, Université Paris-Est, 6 et 8 avenue Blaise Pascal, 77455, Marne-La-Vallée Cedex 2, France

    F. Legoll

  4. INRIA Rocquencourt, MICMAC Team-Project, Domaine de Voluceau, B.P. 105, 78153, Le Chesnay Cedex, France

    X. Blanc, C. Le Bris & F. Legoll

  5. Weierstrass-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117, Berlin, Germany

    C. Patz

Authors
  1. X. Blanc
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  2. C. Le Bris
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  3. F. Legoll
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  4. C. Patz
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Correspondence to X. Blanc.

Additional information

Communicated by A. Mielke.

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Blanc, X., Le Bris, C., Legoll, F. et al. Finite-Temperature Coarse-Graining of One-Dimensional Models: Mathematical Analysis and Computational Approaches. J Nonlinear Sci 20, 241–275 (2010). https://doi.org/10.1007/s00332-009-9057-y

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  • DOI: https://doi.org/10.1007/s00332-009-9057-y

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