text: It is useful to recognize that the only states within ~ of the Fermi level contribute significantly to the entropy. Other states are either fully occupied, , or completely unoccupied, . In either case, these states do not contribute to the entropy. If one assumes that the density of states is constant within  of the Fermi level, one can derive that the electron heat capacity, equal to:
  where  is the density of states (number of levels per unit energy) at the Fermi level. Several other approximations can be made, but they all indicate that the electronic entropy should, to first order, be proportional to the temperature and the density of states at the Fermi level. As the density of states at the Fermi level varies widely between systems, this approximation is a reasonable heuristic for inferring when it may be necessary to include electronic entropy in the thermodynamic description of a system; only systems with large densities of states at the Fermi level should exhibit non-negligible electronic entropy (where large may be approximately defined as ).