[gmx-users] Re: Question about Berendsen thermostat and

[baptista at itqb.unl.pt]

On Thu, 24 Jul 2008, David van der Spoel wrote:

> Michael Shirts wrote:
>>>> Thanks for the tip!
>> You're welcome!
>> 
>>>> That thermostat is really nice and also simple to implement.
>>>> It is now in CVS.
>>> If this thermostat has a stochastic term, is the dynamics still
>>> meaningful then?
>> 
>> Of course it's not!  No thermostat gives physical dynamics.  But at
>> least it gives the canonical distribution at equilibrium!
>
> Well in that case I'm not sure what is more important for me. It depends on 
> the application I presume.
>
> But does the NH chain, the mother of all thermostats, indeed yield correct 
> dynamics?

I would say that the mother and father(!) of all thermostats and barostats 
are in Andersen's 1980 paper, where he proposed both a stochastic 
temperature bath and a deterministic extended-system pressure bath (latter 
nicely adapted by Nose to the temperature case). As far as I know, this 
was the first time that someone came out with methods that can be shown to 
(asymptoticaly) sample from the proper ensembles, going beyond the simple 
ad hoc velocity-scaling and similar methods previously used (the 
grandparents :)

As Michael already noted, there are really no true dynamics except in a 
constant-energy method (well, if there is anything "true" in a system with 
periodic boundaries...) For example, in an extended-system heat bath (eg, 
Nose) only the extended system has "true" dynamics, since its trajectory 
is microcanonical. And although the projection of that extended 
microcanonical distribution onto the original (non-extended) space turns 
out to be canonical, there is no reason why the dynamics should be 
preserved after the projection. This is usually not a problem because you 
often just want to get a decent canonical sampling (unless you are trying 
to measure temporal properties, of course). In practice, it turns out that 
you can always fiddle with the values of the time-related parameters of 
the bath ("piston masses" in extended-system methods, "collision 
frequencies" in stochastic methods) until you get a good temporal behavior 
(though you should always keep in mind that those values may be 
system-dependent).

Besides time, we usually don't really care about velocities. Therefore, a 
quite simple procedure is to keep the "instantaneous temperature" (ie, 
kinetic energy) fixed using Gauss' principle of least constraint. Although 
that may sound unphysical, it is easy to show from the Liouville equation 
that the positions strictly follow a canonical distribution (this can be 
found somewhere in one of Denis Evans' 1980's papers). As far as I 
remember, there are no parameters of any sort in this isokinetic 
thermostat and the equations of motion are quite simple. If anyone wants 
to implement it... :)

Best,
Antonio

>
> (I realize I should know all this, but hey...)
>
>> 
>> Best,
>> Michael
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>
>
> -- 
> David van der Spoel, Ph.D., Professor of Biology
> Molec. Biophys. group, Dept. of Cell & Molec. Biol., Uppsala University.
> Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205. Fax: +4618511755.
> spoel at xray.bmc.uu.se	spoel at gromacs.org   http://folding.bmc.uu.se
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--
Antonio M. Baptista
Instituto de Tecnologia Quimica e Biologica, Universidade Nova de Lisboa
Av. da Republica - EAN, Apartado 127
2780-157 Oeiras, Portugal
phone: +351-214469619         email: baptista at itqb.unl.pt
fax:   +351-214411277         WWW:   http://www.itqb.unl.pt/~baptista
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