Considering the potential applications of continuously rotating detonation (CRD) combustors in gas turbines, this paper performed a numerical investigation into the pressure gain performance of CRD combustors, using methane-air as a reactive mixture and under the operating conditions of a micro gas turbine. To analyze the formation process of CRD waves, the variation characteristics of several typical thermodynamic parameters involving thermal efficiency, pressure ratio, and available energy loss were discussed in terms of time and space scales. Numerical results showed that the pressure gain characteristics of the CRD combustors was associated with the corresponding change in Gibbs free energy. Compared to approximate constant pressure-based combustors, usually used in the gas turbines studied, CRD combustors with lower Gibbs free energy loss could offer a significant advantage in terms of pressure ratio. It was found that detonation waves played an important role in increasing pressure ratios but that oblique shock waves caused the loss of extra Gibbs free energy. Due to the changing oblique shock wave height, the effects of CRD combustor axial length on pressure ratios and Gibbs free energy loss were more significant than the effects on detonation wave propagating characteristics and combustion thermal efficiency. When the axial length was changed from 200 mm to 100 mm, the pressure ratio increased by approximately 15.8%.