[gmx-users] size dependence of fluctuations

Mark Abraham Mark.Abraham at anu.edu.au
Mon Oct 5 13:46:42 CEST 2009

```Zuzana Benkova wrote:
> Dear GROMACS users,
>
> most likely I am asking a trivial question but I need to be sure about
> it for calculations of heat capacity based on the fluctuations of energy
> in canonical ensemble. I am doing simulation of water using TIP4P model.
> I compare two systems consisting of 216 and 8*216 = 1728 molecules. The
> expected fluctuations for the larger system should be reduced
> 8^(1/2)=2.83 times with respect to the fluctuations of the smaller
> system. Actually, this applies only to the fluctuations in intensive
> properties such as the temperature, pressure and density while the
> fluctuations in extensive properties such as energies exceed about 2.83
> times the corresponding fluctuations for smaller system. Could you
> explain me the inverse ratio of fluctuations?

Have you simulated long enough that you can measure these fluctuations
reliably? Look at the trend in their behaviour with increasing time.

> I have also one question regarding the heat capacity calculation. If I
> want to apply the formula for canonical ensemble (<E^2>-<E>^2)/(kbT^2)
> than the capacity should be size dependent. I am a bit puzzled about it
> and any explanation would be very helpful for me. Thanks in advance

Heat capacity is extensive. Quoting the output that's confusing you