amep.thermo.kintemp

amep.thermo.kintemp(v: ndarray, m: float | None | ndarray = None, d: int = 2) → ndarray

Calculates the kinetic temperature per particle based on the 2nd moment of the velocity distribution as described in Ref. [1].

Notes

The kinetic temperature is defined as the kinetic energy. In the overdamped regime (i.e. mass=0), it is simply \(\langle v^2\rangle\) (see Ref. [2]).

References

[1]

L. Hecht, L. Caprini, H. Löwen, and B. Liebchen, How to Define Temperature in Active Systems?, J. Chem. Phys. 161, 224904 (2024). https://doi.org/10.1063/5.0234370

[2]

Caprini, L., & Marini Bettolo Marconi, U. (2020). Active matter at high density: Velocity distribution and kinetic temperature. The Journal of Chemical Physics, 153(18), 184901. https://doi.org/10.1063/5.0029710

Parameters:

• v (np.ndarray) – Velocity array of shape (N,3).

• m (float or np.ndarray or None, optional) – Particle mass(es). The default is None.

• d (int, optional) – Spatial dimension. The default is 2.

Returns:

temp – Kinetic temperature of each particle. Same length as v.

Return type:

np.ndarray

Examples

>>> import amep
>>> traj = amep.load.traj("../examples/data/lammps.h5amep")
>>> frame = traj[-1]
>>> tkin = amep.thermo.kintemp(
...     frame.velocities(), m=frame.mass()
... )
>>> fig, axs = amep.plot.new(figsize=(3.6,3))
>>> mp = amep.plot.particles(
...     axs, frame.coords(), frame.box, frame.radius(),
...     values=tkin, cscale="log"
... )
>>> axs.set_xlabel(r'$x$')
>>> axs.set_ylabel(r'$y$')
>>> cax = amep.plot.add_colorbar(
...     fig, axs, mp, label=r"$T_{\rm kin}$"
... )
>>> fig.savefig('./figures/thermo/thermo-kintemp.png')
>>>