We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a 5-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to non-exotic, and non-exotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the "cooling" or "heating" effect that follows from the reduced density of photon 2 when a measurement is performed on photon 1.