This paper is devoted to discussing the difference in the thermodynamic entropy budget per baryon in each type of stellar object found in the Universe. We track and discuss the actual decrease of the stored baryonic thermodynamic entropy from the most primitive molecular cloud up to the final fate of matter in black holes, passing through evolved states of matter as found in white dwarfs and neutron stars. We then discuss the case of actual stars with different masses throughout their evolution, clarifying the role of the virial equilibrium condition for the decrease in entropy and related issues. Finally, we discuss the role of gravity in driving the composition and the structural changes of stars with different Main Sequence masses during their evolution up to the final product. Particularly, we discuss the entropy of a black hole in this context arguing that the dramatic increase in its entropy, differently from the other cases, is due to the gravitational field itself.