On the relationship among Ghosh-Berkowitz-Parr entropy, Shannon entropy and Fisher information

Abstract

In their seminal work thirty years ago, Ghosh, Berkowitz, and Parr reformulated the ground-state density-functional theory into a local version of thermodynamics, where a new concept, called Ghosh-Berkowitz-Parr entropy, was proposed. Employing the non-interacting kinetic energy density and Thomas-Fermi kinetic energy density, this entropy was formulated like the Sackur-Tetrode equation in classical thermodynamics. Not much has been known about its properties. In this contribution, we investigate its relationship with Shannon entropy and Fisher information from the numerical perspective. To that end, we have examined 36 neutral atoms and 42 molecular systems. We have considered both molecular and atomic contributions with Bader’s zero-flux criterion to partition atoms in molecules. Our results show that these quantities are closely correlated, and yet their correlations might be complicated since no universal relationship among them has been observed.