[gmx-users] Rerefence on Berendsen vs Nose-Hoover

[Jochen Hub]

Hi John,

thanks a lot for your comments. I will have a closer look on the paper 
that you mentioned.

Cheers,
Jochen

John D. Chodera wrote:
> Hi Jochen,
>
> I think the paper you are referring to is this one, commonly cited on 
> the AMBER mailing list and by others in support of the idea that there 
> is little difference between Berendsen and Nose-Hoover:
>
> * T. Morishita. Fluctuation formulas in molecular-dynamics simulations 
> with the weak coupling heat bath. J. Chem. Phys., 113(8):2976, 2000.
>
> However, this paper actually concludes the opposite:
>
> "The present study shows that the WC thermostat does not produce the 
> canonical ensemble but another ensemble."
>
> The paper demonstrates that, in the limit as the coupling time \tau -> 
> 0, the isokinetic ensemble is produced, while in the limit that \tau 
> -> \infinity, the microcanonical ensemble is produced.
>
> For expectations involving only coordinates (and not momenta), the 
> agreement with the canonical ensemble is achieved only if terms on the 
> order of 1/N are neglected -- which is precisely the rate at which all 
> ensembles become equivalent, the "thermodynamic limit". In other 
> words, if your system is big enough to reach the "thermodynamic limit" 
> (and who knows how big that is?) then you are just as well off using 
> *any* ensemble -- NVE, NPT, NPH, NVT -- it doesn't matter anymore.
>
> Allen and Tildesley, for example, states on the difference between 
> ensembles: "the small relative magnitude of the correction term can be 
> seen explicitly: it decreases as O(N^-1)." (pg. 45 in my edition)
>
> So only in the thermodynamic limit will there be correspondence 
> between Berendsen and Nose-Hoover ensembles for properties dependent 
> on the configuration space distribution. Whether your system is large 
> enough to have reached this limit is something that you will have to 
> establish for yourself.
>
> However, if you are interested in kinetic properties and make use of 
> the Berendsen weak-coupling algorithm, you will likely want to 
> investigate whether there is any \tau dependence in your computed 
> properties or observed behavior, since the width of the kinetic energy 
> distribution is a strong function of \tau.
>
> Cheers,
>
> - John
>
> -- 
> Dr. John D. Chodera <jchodera at gmail.com> | Mobile : 415.867.7384
> Postdoctoral researcher, Pande lab | Lab phone : 650.723.1097
> Department of Chemistry, Stanford University | Lab fax : 650.724.4021
> http://www.dillgroup.ucsf.edu/~jchodera
>>
>> Date: Mon, 15 Oct 2007 15:37:40 +0200
>> From: Jochen Hub <jhub at gwdg.de>
>> Subject:
>> To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>> Message-ID: <47136D24.8070103 at gwdg.de>
>> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>>
>> Hi,
>>
>> I think there is a paper around which says that for parcticle purposes
>> it hardly matters whether one uses Berendsen or Nose-Hoover T-coupling.
>> Does anyone remember the reference?
>>
>> Thanks in advance,
>> Jochen
>>
>> --************************************************
>> Jochen Hub
>> Max Planck Institute for Biophysical Chemistry
>> Computational biomolecular dynamics group
>> Am Fassberg 11
>> D-37077 Goettingen, Germany
>> Email: jhub[at]gwdg.de
>> ************************************************
>>
>>
>
> .
>


-- 
************************************************
Jochen Hub
Max Planck Institute for Biophysical Chemistry
Computational biomolecular dynamics group
Am Fassberg 11
D-37077 Goettingen, Germany
Email: jhub[at]gwdg.de
************************************************