# Entropy parameter#

The entropy parameter was introduced by Piaggi et al [1] for identification of defects and distinction between solid and liquid. The entropy paramater \(s_s^i\) is defined as,

where \(r_m\) is the upper bound of integration and \(g_m^i\) is radial distribution function centered on atom \(i\),

\(r_{ij}\) is the interatomic distance between atom \(i\) and its neighbors \(j\) and \(\sigma\) is a broadening parameter.

The averaged version of entropy parameters \(\bar{s}_s^i\) can be calculated by using a simple averaging over the neighbors given by,

Entropy parameters can be calculated in pyscal using the following code,

```
from pyscal3 import System
sys = System('conf.dump')
sys.find.neighbors(method="cutoff", cutoff=0)
lattice_constant=4.00
avg_entropy = sys.calculate.entropy(1.4*lattice_constant, averaged=True)
```

The value of \(r_m\) is provided in units of lattice constant. Further parameters shown above, such as \(\sigma\) can be specified using the various keyword arguments.

In pyscal, a slightly different version of \(s_s^i\) is calculated. This is given by,

The prefactor \(2\pi k_B\) is dropped in the entropy values calculated in pyscal.

## References#

Piaggi, P. M. & Parrinello, M. Entropy based fingerprint for local crystalline order. Journal of Chemical Physics 147, (2017).