Information Loss in Coarse-Graining of Stochastic Particle Dynamics

• Published in: Journal of statistical physics Vol. 122; no. 1; pp. 115 - 135
• Main Authors: Katsoulakis, Markos A., Trashorras, José
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.01.2006; Springer Nature B.V; Springer Verlag
• Subjects: Adsorption; Algorithms; Approximation; Coarsening; Desorption; Errors; Exact sciences and technology; Finite difference method; Finite element method; Granulation; Intermolecular forces; Mathematics; Partial differential equations; Physics; Probability; Statistical physics, thermodynamics, and nonlinear dynamical systems; Stochastic models; Stochastic processes; Markov process; Stochastic model; Partial differential equations; Particle motion; Stochastic processes; Entropy; Hierarchy; Monte Carlo methods; Information loss. MSC subject classifications: 82C80; Coarse-grained Monte Carlo methods; Particle system; Classification; Particle scattering; 94A17; 60J22; Fluctuations; Interacting particle systems; Desorption; Microscopic model; Space-time; Algorithms; Adsorption; Lattice dynamics; Lattice model; Markov processes; Mesoscopic systems
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-005-8063-1

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.