On Sun, Apr 02, 2017, Michael R Shirts wrote:
>
> In the limit of long enough time, the temperature distribution of
> Andersen is indeed the canonical distribution.
Just a few quick points, from very much a non-expert:
1. The ntt=2 option in Amber is rather different from the thermostat
proposed by Andersen in 1980. (The upcoming Amber 2017 Reference
Manual will be revised to make this clearer.) In Amber, setting
ntt=2 simply automates the process of running as series of NVE
simulations, starting from the coordinates at the end of the previous
simulation, and velocities chosen from a Maxwell-Boltzmann distribution
at the desired temperature.
2. As Leimkuhler and Matthews emphasize in their book "Molecular
Dynamics", the rate and degree to which coordinates sample a canonical
distribution can be quite independent of the rate and degree to which
the momenta are correctly sampled. Most simulations in our field (say
for free energy estimation) rely more heavily on getting the proper
distribution of conformations than on the proper distribution of
momemta.
A well-known example of this arises for various flavors of Langevin
dynamics schemes when applied to a harmonic oscillator. With a finite
time step you can get the correct distribution of coordinates, or the
correct distribution of momenta, but not both at the same time.
3. "Proofs" that a given thermostat yields (or fails to yield) a canonical
distribution generally assume that the dynamics is propagated correctly,
which will not be true with finite time steps. Numerical tests, like
those described by Michael Shirts, or against "gold standard" simulations
run with very small time steps, are generally required for any practical
integration protocol.
....dac
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Received on Sun Apr 02 2017 - 10:30:03 PDT
