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. Introduction. -Low-dimensional electronic devices are important building blocks for quantum electronics. This is one of the reasons of great interest to these systems. Another reason is that size quantization of the electronic states in low-dimensional systems leads to quantization of their thermal and transport properties. The most famous are the integer [1] and fractional [2] quantum Hall effect in two-dimensional electron gas (2DEG) and conductance quantization of quasi-one-dimensional channels [3].In this Letter, we address the major thermodynamic quantity -entropy -of a quasi-two-dimensional electron gas. An elegant way to measure directly the entropy per electron, s ≡ (∂S/∂n) T , was recently demonstrated [4]. Here T is temperature. We will show that the quantization of the energy spectrum of quasi-2DEG into subbands leads to a very specific quantization of the entropy: s exhibits sharp maxima as the chemical potential µ passes through the bottoms of size quantization subbands (E i ). The value of the entropy in the N -th maximum depends only on the number of the maximum, N :