# [gmx-developers] Drift in Conserved-Energy with Nose-Hoover thermostat

Shirts, Michael R. (mrs5pt) mrs5pt at eservices.virginia.edu
Mon Jul 20 00:55:47 CEST 2015

```> Do I have to switch to double precision if I care about energy conservation, integrator symplecticity, phase space volume conservation and ergodicity?

This sounds a like a good idea.  If you are doing tests where this matters, use double precision. Sounds like the safest.

> Since bigger round-off errors by reduced precision shouldn't accumulate linearly but at worst with Sqrt(N): Shouldn't one be worried about the occurence of a linear systematic error by only changing the precision from double to single in a calculation?

Reduced precision errors only would be linear if the errors are uncorrelated, but it's not clear to me why roundoff errors would be uncorrelated.

> But if you have a constant downward drift of energy you must consider that there is less phase space volume at lower energies - so there is no volume conservation in phase space.

Correct, for NVE.  For NVT,  the conserved energy is a bookkeeping number, it has nothing to do with the current phase space of the system. The thermostat is pumping in more energy so that the kinetic energy remains consistent with the desired temperature.  We then actually have a steady state system, rather than an equilibrium system.  The question is, how different is this distribution from the true equilibrium distribution?

This is generally testable.  For thermodynamic  calculations (which is what one presumably is intrested in with a thermostat, rather than the dynamics ), what really matters is 1) whether the correct distribution is obtained within noise and 2) whether the sampling is ergodic.  2) is very hard to answer, but 1) can be checked by

https://github.com/shirtsgroup/checkensemble

With the theory described here:

http://dx.doi.org/10.1021/ct300688p

Gromacs in single precisions seems to behave fine statistically for systems of a few hundred atoms.

I suspect that there are subtle phenomena where the lack of exact symplecticness matters.  I also believe from my testing (no full paper on this) that there aren't very many that occur in highly chaotic systems with hundreds of particles at NIT.

I bet there are cases with just a few particles where the problems could become very obvious, however.

Best,
~~~~~~~~~~~~
Michael Shirts
Associate Professor
Department of Chemical Engineering
University of Virginia
michael.shirts at virginia.edu<mailto:michael.shirts at virginia.edu>
(434) 243-1821

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