title: High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations.
abstract: We introduce high-order formulas for the computation of statistical averages based on the long-time simulation of molecular dynamics trajectories. In some cases, this allows us to significantly improve the convergence rate of time averages toward ensemble averages. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give some error bounds that allow one to fix the parameters of the computation in order to reach a given desired accuracy in the most efficient manner.
authors.affiliation: CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, Cité Descartes, 77455 Marne-la-Vallée Cedex 2, France. cances@cermics.enpc.fr
authors.forename: Eric
authors.initials: E
authors.lastname: Cancès
authors.forename: François
authors.initials: F
authors.lastname: Castella
authors.forename: Philippe
authors.initials: P
authors.lastname: Chartier
authors.forename: Erwan
authors.initials: E
authors.lastname: Faou
authors.forename: Claude
authors.initials: C
authors.lastname: Le Bris
authors.forename: Frédéric
authors.initials: F
authors.lastname: Legoll
authors.forename: Gabriel
authors.initials: G
authors.lastname: Turinici