Gravitational quantum well as an effective quantum heat engine

In this work the gravitational quantum well is used to model an effective two-level system and to perform two thermodynamic cycles, the isogravitational and the isoenergetic ones. It is shown that the isogravitational is independent of the scale parameter whereas the isoenergetic has a dependence on the eigenstates chosen to form the cycle. An equivalent equation for the isoenergetic cycle is also obtained, which is similar to the equation of state for an isothermal process of an ideal gas. This equation reinforces the concept of energy bath, where the temperature is replaced by the energy into the expression of efficiency.