Information entropy and Thomas-Fermi theory

Informational entropies Sρ =-∫ρlnρdr→ and Sγ =-∫γlnγdp→ have been computed from neutralatom Thomas-Fermi coordinate-space density γ and momentum density ρ. These entropies turn out to be Sρ≃N(5.59-2lnN) and Sγ≃N(1.06+lnN) leading to Sρ +Sγ ≃N(6.65-lnN), strikingly similar in form to the rigorous bound Sρ +Sγ >=3N(1+lnpπ)-2NlnN due to Bialynicki-Birula and Mycielski. It is conjectured that the informational entropies for atoms may be well represented by S≃N(α+β lnN), α and β , being universal constants