Phase-space Fisher information

Ágnes Nagy

Juan Carlos Bolívar, Ágnes Nagy, E. Romera

It is shown that phase-space Fisher information marks topological phase transitions in 2D Dirac gapped materials. The phase-space Fisher information determined for electrons and holes exhibit minimum at the charge neutrality points. Topological quantum numbers are defined to identify different phases utilizing combined information measures. Upper and lower bounds are derived for the phase-space Fisher information.

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.

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.