title: Probabilistic Derivation of Spatiotemporal Correlation Functions in the Hydrodynamic Limit.
abstract: In this paper, we use probability theory to prove in suitable conditions the equivalence of equilibrium time correlation functions of microscopic density fields with the time correlation functions of local macroscopic density fields evolved by hydrodynamics in (approximate) phenomenological continuum theories of matter. We further discuss a useful and rigorous numerical algorithm, derived from this framework, to compute macroscopic space- and time-dependent behaviors (such as the hydrodynamical one) via molecular dynamics simulations.
authors.affiliation: Dipartimento di Fisica, University of Roma "La Sapienza" , Rome, 00185 Italy.|School of Physics, University College Dublin , Belfield, Dublin, 4 Ireland.
authors.forename: Giovanni
authors.initials: G
authors.lastname: Ciccotti
authors.affiliation: CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne , 1015 Lausanne, Switzerland.
authors.forename: Sara
authors.initials: S
authors.lastname: Bonella
authors.affiliation: Dipartimento di Scienze Fisiche, Informatiche e Matematiche, University of Modena and Reggio Emilia , 41121 Modena, Italy.
authors.forename: Mauro
authors.initials: M
authors.lastname: Ferrario
authors.affiliation: Dipartimento di Scienze Fisiche e Chimiche, University of L'Aquila , 67100 L'Aquila, Italy.
authors.forename: Carlo
authors.initials: C
authors.lastname: Pierleoni