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Re: [lammps-users] Per atom temperature
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Re: [lammps-users] Per atom temperature

From: Axel Kohlmeyer <akohlmey@...24...>
Date: Tue, 15 Aug 2017 07:10:56 -0400

On Tue, Aug 15, 2017 at 6:29 AM, Nader Ameli <nader.mechanic@...24...> wrote:
Dear Ramaswami,
Many thanks for your point. I have read from Axel that "temperature" is not a well parameter for a small group of atoms, and it is better we use an average temperature for our system (by "compute temp" or "thermo_style temp" commands). However, I have seen in the recent articles that researchers present temperature distribution (an example is attached). 
I got kinetic energy of my system (either per atom and total system); nevertheless, I would like to obtain its temperature distribution. 
Stefan kindly recommended that I divided out the appropriate DOF per atoms. What is your idea about this? How can I use this if a couple of my particles are fixed and the rest of them are free in movement?
I look forward to receiving your hints.

​please use common sense here. of course, you can apply the formula to compute a (microscopic) temperature Sum_i (1/2 * m * v**2 * k_B​) / N_DOF also to a group of 1 atom. the result doesn't really correspond to the thermodynamic concept of a temperature, though. what you are really looking at is the instantaneous kinetic energy mapped to a temperature scale. at any rate, this is easy to implement with an atom style variable. i recommend you freshen up your statistical thermodynamics knowledge and check out particularly the meaning of ensemble averages and time averages and their relation to macroscopic thermodynamic properties.

next comment i have is about your term "distribution". you are not very precise here and thus it is very difficult to give meaningful advice. distribution can mean a spatial distribution or a distribution by value, i.e. a histogram. also, a spatial distribution can be computed for and averaged over space in 1d, 2d, or 3d set of bins or through color-coding individual points/atoms.

in the picture you attached uses the term "distribution" in the sense of a spatial distribution.
but it would be more precise to talk about color coded visualization of a snapshot, where the color if individual atoms is mapped to their kinetic energy (and the kinetic energy measured in units corresponding to a temperature). this is easy to do with many visualization programs. you can dump the positions *and* velocities and simply visualize the system color codes by velocity (if all atoms have the same mass or by velocity times mass) and then simply recompute from the _expression_ above which temperature which kinetic energy corresponds to and then use that for your legend. of course, you can also just compute the atom style variable mentioned above and add that to your dump. in the end this is a (advanced?) visualization problem, not really a LAMMPS problem.

i don't understand your last question: if an atom is immobile, its velocity will not matter and would normally be zero, so where is the problem with that? you just visualize your system and be done with it. where is the need to turn this into a big philosophical discussion?




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Dr. Axel Kohlmeyer  akohlmey@...12...24...
College of Science & Technology, Temple University, Philadelphia PA, USA
International Centre for Theoretical Physics, Trieste. Italy.