[gmx-users] size dependence of fluctuations

Zuzana Benkova upolzben at savba.sk
Fri Oct 2 14:25:16 CEST 2009

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

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




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