Thermodynamics of normal and BCS systems at the Fermi energy near the logarithmic singularity of DOS

The thermodynamics of Fermi particles in the band with the central logarithmic peak of DOS is discussed. This is accomplished if the absolute value of the difference of the Fermi energy and the energy of the peak of DOS is much smaller or much bigger than the temperature T, in units of energy. The T-dependence of the chemical potential is obtained, for s and p paired BCS systems, for low and subcritical T, as well as for normal systems. It leads, for superconducting systems, to a first order phase transition and to deviation of the Fermi surface caused by pairing.