  We demonstrate that the partial entropy of a two-dimensional electron gas
(2DEG) exhibits quantized peaks at resonances between the chemical potential
and electron levels of size quantization. In the limit of no scattering, the
peaks depend only on the subband quantization number and are independent on
material parameters, shape of the confining potential, electron effective mass
and temperature. The quantization of partial entropy is a signature of a
topological phase transition in a 2DEG. In the presence of stationary disorder,
the magnitude of peaks decreases. Its deviation from the quantized values is a
direct measure of the disorder induced smearing of the electronic density of
states.
