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

Berk Hess gmx3 at hotmail.com
Fri Jul 25 09:34:32 CEST 2008

```Hi,

The reason for the less-affected dynamics has been mentioned before in this thread.
The rescaling thermostat is first order: exponential decay plus a stochastic term,
while NH is second order. NH will always produce artificial oscillations.
I think this rescaling thermostat is the thermostat which will influence the dynamics
the least of all possible thermostats.

Another advantage over plain NH is ergodicity.

Berk.

From: michel.cuendet at isb-sib.ch
Date: Thu, 24 Jul 2008 21:49:58 +0200
To: gmx-users at gromacs.org
Subject: [gmx-users] Re: Question about Berendsen thermostat	and Nose-Hoover	temp coupling

Hi all,
Very interesting discussion ! Here are a few thoughts on two points that appeared in the last digest:
David: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".
Berk: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.
Cheers,Michel
==========================================================Michel Cuendet, Ph.DMolecular Modeling GroupSwiss Institute of BioinformaticsCH-1015 LausanneSwitzerlandhttp://ludwig-sun1.unil.ch/~mcuendet/==========================================================

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