Determining entropy (and free energy) of system

User discussions
1

GROMACS version: 2021.3
GROMACS modification: No

Hi,

I’ve run some simulations, with the box made up of 100 molecules, with each molecule having 20-22 beads (I’m using a Coarse-Grained Force Field). I’d now like to find the entropy of the whole box at different time-points along the trajectory, as I would then like to use this find the Gibbs free energy of the system at the different time-points (not the Free Energy difference), using the equation G = U - TS + pV. U, T and pV at the different time-points are easily obtainable using gmx energy, but I’m definitely finding S more tricky.

I’ve read the discussions on here and researchgate, and (I think) I understand that I need to use gmx covar followed by gmx anaeig to extract the entropy of the system. However, I’m really struggling with how to do this, what flags to use and so on. For example,

  • should I use the -mwa flag when running gmx covar?
  • for the -b and -e flags, should I just the same value in both, i.e. the single time-point I’m interested in, and then change this for each time-point I’m interested in?
  • given that I want to calculate the entropy for the whole system, when I run gmx covar, should I choose “System” when asked to select a group for least-squares fit and for the covariance analysis?

Taking a step back… do I need to do any transformation to the trajectory before I even run gmx covar?

I’m a novice with trying to determine entropy like this, so any help, especially line commands, would be very appreciated.

Thanks,

Robert

2

Usually one does not want absolute entropies and free-energies, but relative. Why do you want the absolute versions?

Entropies and free-energy are properties of a thermodynamic state of the system and can not be computed as a function of time.

3

Thanks for your reply. I’m trying to look at a system in both the solid and liquid state at different temperatures (so start with the system in the solid state, equilibrate at different temperatures still in solid state, melt it out at high temperature, then equilibrate again at different temperatures while still in the liquid state), then calculate the free energies at the different temperatures/states and compare, and then determine the equilibrium point, i.e. the point at which the free energies are the same (i.e. the melting point).

Any suggestions on how to do this if I’m going about it incorrectly would be greatly appreciated.

4

That sounds like a very challenging problem. You need significant expertise for that. I don’t know what the best approach would be. This is not a “simple” question that can be answered with a short post on a forum.