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Effective dynamics using conditional expectations
"... Abstract. The question of coarsegraining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarsegrained variable ξ(x), where x describes the configuration of the system in a highdimensional space R n, and ξ is a smooth ..."
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Abstract. The question of coarsegraining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarsegrained variable ξ(x), where x describes the configuration of the system in a highdimensional space R n, and ξ is a smooth function with value in R (typically a reaction coordinate). It is well known that, given a BoltzmannGibbs distribution on x ∈ R n, the equilibrium properties on ξ(x) are completely determined by the free energy. On the other hand, the question of the effective dynamics on ξ(x) is much more difficult to address. Starting from an overdamped Langevin equation on x ∈ R n, we propose an effective dynamics for ξ(x) ∈ R using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarsegrained dynamics. AMS classification scheme numbers: 35B40, 82C31, 60H10Effective dynamics using conditional expectations 2 1.
Local AronsonBénilan estimates and entropy formulae for porous medium and fast . . .
, 2008
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Decay of covariances, uniqueness of ergodic component and scaling limit for a class of ∇φ systems with nonconvex potential
, 2009
"... We consider a gradient interface model on the lattice with interaction potential which is a nonconvex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show for a class of nonconvex potentials: the uniqueness of ergod ..."
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Cited by 1 (1 self)
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We consider a gradient interface model on the lattice with interaction potential which is a nonconvex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show for a class of nonconvex potentials: the uniqueness of ergodic component for ∇φ Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.
Invariances in variance estimates
, 2011
"... We provide variants and improvements of the BrascampLieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for logconcave measures with many symmetries and to noninteracting conservative spin systems. 1 ..."
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We provide variants and improvements of the BrascampLieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for logconcave measures with many symmetries and to noninteracting conservative spin systems. 1