Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches

Xavier Blanc; Claude Le Bris; Frédéric Legoll; Carsten Patz

inria-00282107, version 2

Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches

Xavier Blanc ^1, 2, Claude Le Bris () ^1, 3, Frédéric Legoll () ^1, 4, 5, Carsten Patz ⁶

Journal of Nonlinear Science 20, 2 (2010) 241-275

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.

1: MICMAC (INRIA Paris - Rocquencourt)
Ecole des Ponts ParisTech – INRIA
2: Laboratoire Jacques-Louis Lions (LJLL)
CNRS : UMR7598 – Université Pierre et Marie Curie (UPMC) - Paris VI
3: Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
INRIA – Ecole des Ponts ParisTech
4: Laboratoire d'Analyse des Matériaux et Identification (LAMI)
Institut Navier – LCPC – Ecole des Ponts ParisTech
5: Laboratoire Navier
Ecole des Ponts ParisTech – CNRS : UMR8205 – IFSTTAR
6: WIAS Berlin
WIAS Berlin

inria-00282107, version 2
http://hal.inria.fr/inria-00282107
oai:hal.inria.fr:inria-00282107
From: Frederic Legoll <>
Submitted on: Wednesday, 28 May 2008 13:05:16
Updated on: Friday, 23 September 2011 10:45:32

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