Szilard's information heat engines in the deep quantum regime

We investigate Szilard's information heat engine in the deep quantum regime. If the ground state is non-degenerate, the work extracted from the engine divided by temperature, ~S, vanishes as the temperature approaches zero, where the third law of thermodynamics manifests itself in information science. The degenerate ground state induced by the symmetry or by accident gives rise to non-zero ~S at zero temperature. Based upon these two rules, namely the third law and the degenerate ground state, we can understand the low-temperature behavior of the quantum Szilard engine in various physical situations such as an engine consisting of either bosons or fermions either with or without interactions.