Information Loss in Coarse-Graining of Stochastic Particle Dynamics |
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Authors: | Markos A Katsoulakis José Trashorras |
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Institution: | (1) Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305, USA;(2) CEREMADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France;(3) CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France |
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Abstract: | Recently a new class of approximating 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(12,13,15). 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 in terms of specific relative entropy the information loss between non-equilibrium exact and approximating
coarse-grained adsorption/desorption lattice dynamics. Our result is an error estimate analogous to rigorous error estimates
for finite element/finite difference approximations of Partial Differential Equations. We prove this error to be small as
long as the level of coarsening is small compared to the range of interaction of the microscopic model. This result gives
a first mathematical reasoning for the parameter regimes for which approximating coarse-grained Monte Carlo algorithms are
expected to give errors within a given tolerance.
MSC (2000) subject classifications: 82C80; 60J22; 94A17 |
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Keywords: | Coarse-grained Monte Carlo methods Markov processes Interacting particle systems Information loss |
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