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

Bernhard b.reuter at uni-kassel.de
Tue Jul 21 14:43:28 CEST 2015

Dear Michael,

thank you very much for your very helpfull answer.
Obviously we agree on the dubious nature of the linear drift and that 
its origin from reduced precision round-off errors is doubtful.
In my opinion the occurence of a linear energy drift of this size could 
indicate a bug in the program.
So I startet a more rigorous investigation and would like to share some 
preliminary results:

Graph of Verlet buffer-size vs. energy-drift size for single and double 

Graph of the linear total energy drift for a buffer-size of 0.02nm:

Exemplary mdp and log files for a buffer-size of 0.02nm:

The investigated protein-water system consists of 22765 atoms, the 
AMBER99SB-ILDN force field with TIP3P water was used, all simulations 
were in the NVE-ensemble, GROMACS 4.6.7 was used.

I will repeat the tests with GROMACS 5.0 and for different test systems 
(i.e. the lysozyme system from the popular lysozyme tutorial of Justin 


Am 20/07/15 um 00:50 schrieb Shirts, Michael R. (mrs5pt):
> > 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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