# AMBER Archive (2006)Subject: Re: AMBER: Temperature fluctuation with Langevin Temperature control

From: David A. Case (case_at_scripps.edu)
Date: Mon Aug 28 2006 - 12:32:08 CDT

On Sun, Aug 27, 2006, Adrian Roitberg wrote:

> Why do you think 4K is too much of a fluctuation ?
>
> I think you need to understand the langevin thermostat a bit better
> before you can say that 4 K is too much, too little or just right.
>

To expand a little on Prof. Roitberg's comments:

It's not so much that you need to learn about the Langevin thermostat per se,
as to think about thermodynamic fluctuations in small systems. The behavior
there is quite different from macroscopic systems. Thermodynamic variables
have fluctuations that can be large for very small systems.

The best description of this that I know of is in Chapter XII of Landau &
Lifshitz, Statistical Physics. They show that, for example,

mean-square-fluctuation in T = kT^2/(mC-sub-v)

Taking a "typical" biomolecule of mass 25 kD and a typical value of C-sub-v
of 0.32 cal/(g-K), one gets a root-mean-square fluctuation (the square root
of the above equation) of 4.7 K. This is pretty close to what you report,
as indeed it should be since the Langevin thermostat is designed to yield a
canonical distribution.

Four notes:

1. This expression (or similar ones involving potential energy) are usually
used to determine C-sub-v from the mean-square flucutations (since the heat
capacity for a given force field might not equal the experimental value).
Hence, you should only use the above value of C-sub-v as a indication of its
general value.

2. As the system gets bigger (and its mass gets larger), the fluctuations in
T become smaller. In the thermodynamic limit, they can be neglected.

3. A nice, short paper that discusses some of the implications of this is
here:

%A A. Cooper
%T Thermodynamic fluctuations in protein molecules
%J Proc. Natl. Acad. Sci. USA
%V 73
%P 2740-2741
%D 1976

4. It is possible to devise simulation schemes in which T is rigorously a
constant, with no fluctuations even in small systems. But this is *not* the
canonical distribution we use, and has not seen much use.

...hope this helps...dac

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