We present an analysis of the equilibrium thermodynamics of two-step metal oxide-based water and carbon dioxide-splitting cycles. Within this theoretical framework, we propose a first-principles computational approach based on density-functional theory (DFT) for evaluating new materials for these cycles. Our treatment of redox-based gas-splitting chemistry is completely general so that the thermodynamic conclusions herein hold for all materials used for such a process and could easily be generalized to any gas as well. We determine the temperature and pressure regimes in which the thermal reduction (TR) and gas-splitting (GS) steps of these cycles are thermodynamically favorable in terms of the enthalpy and entropy of oxide reduction, which represents a useful materials design goal. We show that several driving forces, including low TR pressure and a large positive solid-state entropy of reduction of the oxide, have the potential to enable future, more promising two-step gas-splitting cycles. Finally, we demonstrate a practical computational methodology for efficiently screening new materials for gas-splitting applications and find that first-principles DFT calculations can provide very accurate predictions of high-temperature thermodynamic properties relevant to gas splitting.