Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : Recently a new class of coarsegrained stochastic processes and associated Monte Carlo algorithms were derived directly from microscopic stochastic lattice models for the adsorption\/desorption and diffusion of interacting particles$^{\cite{kmv1,kmv2,kv}}$. The resulting hierarchy of stochastic processes is ordered by the level of coarsening in the space/time dimensions and describes mesoscopic scales while retaining a significant amount of microscopic detail on intermolecular forces and particle fluctuations. Here we rigorously compute the information loss between nonequilibrium microscopic and coarsegrained adsorption\/desorption lattice dynamics. In analogy to rigorous error estimates for finite element\/finite difference approximations of Partial Differential Equations, our result can be viewed as an error analysis between the exact microscopic process and the approximating coarsegrained one, where the error is measured in terms of the specific relative entropy. This estimate gives a first mathematical reasoning for the parameter regimes for which nonequilibrium coarsegrained Monte Carlo algorithms are expected to give errors within a given tolerance. 





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