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Some remarks on free energy and coarse-graining

Abstract : We present recent results on coarse-graining techniques for thermodynamic quantities (canonical averages) and dynamical quantities (averages of path functionals over solutions of overdamped Langevin equations). The question is how to obtain reduced models to compute such quantities, in the specific case when the functional to be averaged only depends on a few degrees of freedom. We mainly review, numerically illustrate and extend results from [3,18], concerning the computation of the stress-strain relation for one-dimensional chains of atoms, and the construction of an effective dynamics for a scalar coarse-grained variable when the complete system evolves according to the overdamped Langevin equation.
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https://hal.archives-ouvertes.fr/hal-00511221
Contributor : Tony Lelièvre Connect in order to contact the contributor
Submitted on : Tuesday, August 24, 2010 - 10:53:34 AM
Last modification on : Friday, February 4, 2022 - 3:20:18 AM

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  • HAL Id : hal-00511221, version 1
  • ARXIV : 1008.3792

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Frédéric Legoll, Tony Lelièvre. Some remarks on free energy and coarse-graining. Engquist, Björn; Runborg, Olof; Tsai, Yen-Hsi R. (Eds.). Numerical analysis and multiscale computations, Springer, 420 p., 2012, Series: Lecture Notes in Computational Science and Engineering, Vol. 82. ⟨hal-00511221⟩

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