Phase space view of quantum mechanical systems and Fisher information

István Hornyák, Ágnes Nagy

Asher Yahalom A

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.

F. Pennini, Angelo Plastino

Ágnes Nagy

Abstract Relationship of Fisher information and density functional theory is reviewed. Links between the Fisher and Shannon information, the local wave‐vector and the relative information are displayed. Euler equations for the Fisher and relative Fisher information are presented. A combined information theoretical and thermodynamic view of density functional theory is analyzed. The extremum of the Shannon and Fisher information results a constant temperature and for Coulomb systems a simple relation between the total energy and phase‐space Fisher information. Relations for phase‐spase fidelity, fidelity susceptibility and relative information are also presented.

James A. Brooke, Franklin E. Schroeck