title: Coarse graining from coarse-grained descriptions.
abstract: We present a generalization of Zwanzig's method of projection operators to the case where the underlying dynamics is not deterministic. The method allows us to perform a coarse graining of an already coarse-grained level of description in which fluctuations are important. The initial level of description is described by a Fokker-Planck equation and, under suitable approximations, the final slower level of description is also described by a Fokker-Planck equation. We illustrate the method for the simple case of the diffusion of colloidal particles at two levels of descriptions.
authors.affiliation: Departmento de Física Fundamental, Universidad Nacional de Educación, Madrid, Spain.
authors.forename: Pep
authors.initials: P
authors.lastname: Español
authors.forename: Federico
authors.initials: F
authors.lastname: Vázquez
mesh_terms: D003102:Colloids / Q000032:analysis* / Q000737:chemistry*; D003198:Computer Simulation; D007700:Kinetics; D008954:Models, Biological; D008956:Models, Chemical; D015233:Models, Statistical; D010316:Particle Size; D011789:Quantum Theory; D012212:Rheology / Q000379:methods*
chemical_list: D003102:Colloids