NVE ensemble with changing temperature

[Lukas Reicht]

Hi,

I want to perform approach-to-equilibrium molecular dynamics (AEMD), where I heat one half of the cell to 250 K and the other half to 350 K. Then, I let the cell equilibrate in an NVE ensemble, meaning that heat will flow from the hot to the cold half, resulting in a cell that has 300 K everywhere. I am interested in the decay of the temperature difference between the hot and cold half, from which I want to calculate the thermal conductivity. I successfully equilibrated the regions to 250 K and 350 K with two separate i-Pi runs and I combined the RESTART files with a Python script.
The problem is about the ensemble temperature in the NVE equilibration run. From equation 3 of https://www.sciencedirect.com/science/article/pii/S001046551300372X, it is clear that the second term of the ring-polymer Hamiltonian depends on the temperature. I assume, that this is the temperature that I set in the input file? For example like:
    <ensemble>
      <temperature units='kelvin'> 300 </temperature>
    </ensemble>

How can I set this temperature correctly? Setting the temperature to 300 K is not correct in my opinion, because this changes the energy associated with the second term of equation 3 (of https://www.sciencedirect.com/science/article/pii/S001046551300372X) abruptly. For example, in the hot region, the temperature in that term would abruptly decrease from 350 K to 300 K. This is associated with a lower energy, which results in a lower kinetic energy and leads to a "jump" in temperature (see attached plot). Likewise for the cold half. This "jump" gets stronger the more beads I use.

I don't know how I should set the ensemble temperature correctly. An ideo would be that I would need to set it to the instantaneous temperature of the hot and cold half, respectively (or a time average thereof).

Best Regards,
Lukas

[Venkat Kapil]

Hi Lukas,

Unfortunately, IMO, the answer to your question depends on which approximation to the quantum Kubo transformed time correlation you are approximating. You may want to follow papers like "https://www.annualreviews.org/doi/10.1146/annurev-physchem-040412-110122" to construct observables or Hamiltonians that correspond to the quantum version of the approach to equilibrium method. My gut says that you will need to set two temperatures with the centroid at the lower and higher temperatures and the non-centroid modes at 300 K in the spirit of centroid molecular dynamics. But the proper way would be to rederive the TRPMD like theory for approach-to-equilibrium dynamics.

Best,
Venkat

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[Michele Ceriotti]

As Venkat says, this is kind of a research question, and not just a matter of implementation. I actually played around for a while with the idea of using TRPMD for heat transport, and came to the conclusion that there is no clean way to define this - if you make the springs temperature or position dependent you get a load of spurious terms.  So basically if you come up with a solution that has some promise on the theoretical front, you'll definitely find someone happy to collaborate on implementing that in i-PI ^_^'

Michele

[Lukas Reicht]

Thanks very much to both of you for your swift replies. I guess it's more complicated than I thought, unfortunately.

Best Regards,

Lukas

[marian...@gmail.com]

Test... (!) 

[marian...@gmail.com]

Hello, I am not sure any of my previous messages were going through, for some strange reason. I try again.

We also toyed with the problem - see https://github.com/mahrossi/i-pi/tree/i-pi-thermo-ben

We never got anywhere meaningful because of a million artefacts when attempting to converge the simulations. My previous messages had more explanations :-D But they have gone to the google void.

This is a sinusoidal temperature profile along one length of the simulation box. We never deemed it meaningful to merge the branch.

[Lukas Reicht]

Interesting, thanks for sharing.

[Venkat Kapil]

Hey Lukas, we have just merged the feature (implemented by Mariana) which allows a separate temperature for the centroid and non-centroid modes in case you want to play around with that.

Just to be clear

* this feature is tested to apply two temperatures on the PI Hamiltonian but what we can't vouch for now as to what exactly this can help. So you will have to try at your own risk. Needless to say we can help out but we highly recommend you to read the theory associated with approximating quantum dynamics in the context of imaginary time paths *

[Lukas Reicht]

Thanks, Venkat. I will take a look at it.