Information entropy and Thomas-Fermi theory

Informational entropies S_ρ=-∫ρlnρd→r and S_γ=-∫γlnγd→p have been computed from neutralatom Thomas-Fermi coordinate-space density ρ and momentum density γ. These entropies turn out to be S_ρN(5.59-2lnN) and S_γN(1.06+lnN) leading to S_ρ+S_γN(6.65-lnN), strikingly similar in form to the rigorous bound S_ρ+S_γ>~3N(1+lnπ)-2NlnN due to Bialynicki-Birula and Mycielski. It is conjectured that the informational entropies for atoms may be well represented by SN(α+βlnN), α and β, being universal constants.