.. _particles-analysis:

Analysis¶

Local entropy¶

The compute_local_entropy operator computes the per-atom entropy as define in ref.

.. code-block:: yaml

compute_local_entropy: rcut: 5.0 ang sigma: 0.15 ang local: true nbins: 50

.. list-table:: :widths: 10 40 10 10 :header-rows: 1

• • Property
  • Description
  • Data Type
  • Default
• • rcut
  • Upper integration limit of Eq. :eq:eq_per_atom_entropy. Distance unit.
  • float
  • \( r_c^{max} \)
• • sigma
  • Broadening parameter. Distance unit.
  • float
  • :math:0.1 \, \AA
• • local
  • If set to true , the \( g_m^i \) is normalized by the local density around atom \( i \).
  • bool
  • true
• • nbins
  • Number of bin on which the integral is discretised.
  • int
  • \(n = \lfloor r_{c} / \sigma \rfloor \)

The per-atom entropy \( s^{i}_{S} \) is computed using the following formula:

.. math:: eq_per_atom_entropy

s^{i}_{S} = -2 \pi \rho k_{B} \int_{0}^{r_{m}} \left[ g^i_m(r) \ln g^i_m(r) - g^i_m(r) + 1 \right] r^2 dr

where \( g^i_m(r) \) is a mollified version of the radial distribution function

.. math:: grm

g^i_m(r) = \frac{1}{4 \pi \rho r^2} \sum_{j \neq i} \frac{1}{\sqrt{ 2 \pi \sigma^2}}\exp^{-(r - r_{ij})^2 / (2 \sigma^2)}

where \( r_{ij} \) is the distance between central atom \( i \) and its neighbour \( j \), and \( \sigma \) is the smoothing parameter.

Local centrosymmetry¶

The compute_local_centrosymmetry operator computes the per-atom entropy as define in ref.

.. code-block:: yaml

compute_local_centrosymmetry: rcut: 5.0 ang nnn: 8