# Multi-time scale integration.

*From*: Guido Germano <g.germano #*at*# bristol.ac.uk>
*Organization*: Physics Department University of Bristol
*Subject*: Multi-time scale integration.
*Date*: Tue, 15 Sep 1998 11:43:33 -0400 (EDT)

> In the literature on multi-time scale integration, a lot of importance is
> placed on time reversibility. Why this is so important is something
> that I have never been able to figure out. If an integration
> algorithm is efficient and produces a small global error then why is
> this not sufficient. If anybody can enlighten me on this subject I
> would appreciate it.
>
> --
> Don Steiger
> dons #*at*# hamilton.math.missouri.edu
Newton's equations are time-reversible, and Hamiltonian dynamics
preserves phase space volume. Non-reversible integration schemes do not
preserve volume in phase space and usually show also long-term energy
drifts. The reasons for wanting time-reversibility are therefore
eminently physical and not mathematical. A good reference is the book by
Daan Frenkel and Berends Smit, "Understanding Molecular Simulation",
Academic Press 1996.
Regards
Dr. Guido Germano
Research Assistant in Theoretical Physics, University of Bristol, England
Tel. +44-117-928 9000 ext. 8755, http://www.phy.bris.ac.uk/staff/germano_g.html