Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : Recently a new class of coarse-grained 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 non-equilibrium microscopic and coarse-grained 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 coarse-grained 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 non-equilibrium coarse-grained Monte Carlo algorithms are expected to give errors within a given tolerance.
 
 
INFORMATION LOSS IN COARSE-GRAINING OF STOCHASTIC PARTICLE DYNAMICS
KATSOULAKIS Markos A., TRASHORRAS José
2004-59
09-11-2004
 
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