Kinetic Energy and Fisher Information

Ian P. Hamilton, Ricardo Antonio Mosna

Carlos Alberto Gomez-Uribe

Ágnes Nagy

The thermodynamic view of density functional theory is extended along the adiabatic path. A particular kinetic-energy-density gauge is selected by minimizing the phase-space Fisher information under fixed density and total kinetic energy. Utilizing this choice, a relation between the correlation energy and the phase-space Fisher information is derived. Monotonic behavior of the minimum phase-space Fisher information along the adiabatic path is proved.

István Hornyák, Ágnes Nagy

Shunlong Luo

By interpolating between Fisher information and mechanical kinetic energy, we introduce a general notion of kinetic energy with respect to a parameter of Schrödinger wavefunctions from a statistical inference perspective. Kinetic energy is the sum of Fisher information and an integral of a parametrized analogue of quantum mechanical current density related to phase. A family of integral inequalities concerning kinetic energy and moments are established, among which the Cramér–Rao inequality and the Weyl–Heisenberg inequality, are special cases. In particular, the integral inequalities involving the negative order moments are relevant to the study of electron systems. Moreover, by specifying the parameter to a scale, we obtain a family of inequalities of uncertainty relation type which incorporate the position and momentum observables symmetrically in a single quantity.

C. A. Onate, M. C. Onyeaju, A. N. Ikot