[gmx-users] Re: Question about Berendsen thermostat and Nose-Hoover temp coupling

Michel Cuendet michel.cuendet at isb-sib.ch
Thu Jul 24 21:49:58 CEST 2008

Hi all,

Very interesting discussion ! Here are a few thoughts on two points  
that appeared in the last digest:

> But does the NH chain, the mother of all thermostats, indeed yield  
> correct dynamics?

No it does not, if what you call correct dynamics is the Hamitlonian  
dynamics corresponding to your H(r,p)= p^2 / 2m + V(q) . If your  
system would follow "correct" Hamiltonian dynamics, the NVE ensemble  
would be sampled. As heat has to be exchange with some reservoir, the  
particle's trajectories have to be perturbed in some way. So I agree  
with Michael Shirts that "No thermostat gives physical dynamics".  
Nobody really knows what the correct coupled dynamics would be...

This is actually a very interesting and quite paradoxical point in  
statistical mechanics. The Boltzmann distribution reads exp(-beta H 
(q,p) ) / Z , but the system particles (at least some of them) can  
actually _not_ evolve according to H(q,p). This difficulty was  
recognized by Boltzmann, who clearly stated early on that he  
deliberately chose to ignore the nature of the coupling between the  
system and the heat bath and call it "weak".

Now our MD simulations usually tend to heat up without thermostat,  
meaning that there are artifacts perturbing the dynamics. Thus the  
effective dynamics is incorrect in the first place, and in this  
regard, the thermostat is not the primary source of "incorrectness".

> The stochastic term works on the "Berendsen scaling parameter" only.
> It has the same correlation time as tau_t.
> So the dynamics is nearly unaffected, surely less than with Nose- 
> Hoover.

In Nosé Hoover, the coupling to the extra degree of freedom also acts  
as a "scaling parameter" or "time dependent friction  
coefficient" (which is common to all particles). It should not make a  
difference whether this coefficient evolves deterministically or  
stochastically? Berk, could you explain why you say that the dynamics  
would be less affected by the "stocahstic Berendsen" than the NH?  
Both thermostats have to impose the same (canonical) temperature  
fluctuations on the system, pumping heat in and out (in case the  
uncoupled dynamics were really conservative). I still need to read  
the Bussi et al. paper, though.


Michel Cuendet, Ph.D
Molecular Modeling Group
Swiss Institute of Bioinformatics
CH-1015 Lausanne

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