Thermodynamics of phonon-stabilized Fermi distributions with application to uranium

Since phonons are built on the free energy of electrons, their frequencies can be altered by thermal electronic excitations, implying that thermal electronic excitations can alter the phonon entropy. The effect of this extra phonon entropy on electronic distribution functions and thermodynamic properties is calculated in the limit of classical vibrations. The phonon entropy stabilizes electrons above the Fermi level by more than the usual k _B T. The thermodynamic coupling of electron and phonon degrees of freedom allows far more heat capacity than in equivalent independent systems. The method developed is used to explain uranium data from the literature.