Information loss in coarse-graining of stochastic particle dynamics
Publication Date
2006
Journal or Book Title
JOURNAL OF STATISTICAL PHYSICS
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.
Pages
115-135
Volume
122
Issue
1
Recommended Citation
Katsoulakis, MA and Trashorras, J, "Information loss in coarse-graining of stochastic particle dynamics" (2006). JOURNAL OF STATISTICAL PHYSICS. 449.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/449
Comments
The published version is located at http://www.springerlink.com/content/f66l62715334n976/