  In the present paper we derive the general expressions for the differential
entropy per particle near van Hove singularities (vHs) in the density of
states. The dependence of entropy per particle on chemical potential and
temperature demonstrates different behavior depending on the type of vHs, and
distinguishes high-order vHs with different divergence exponents and flat
bands. In addition, it allows one to test the ``flatness" of the band in
experiment. We compare the analytic predictions with the numerical calculation
of the differential entropy for tight-binding models of graphene, Lieb lattice
and square-octagon lattice. Our results show that the obtained analytic
expressions capture the main features of the differential entropy, thus serving
as a good probe for details of the density of states structure.
