[gmx-users] size dependence of fluctuations

[Mark Abraham]

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 
would help you get better feedback.

Mark