Carbon-neutral fuel production by solar-driven two-step thermochemical carbon dioxide splitting provides an alternative to fossil fuels as well as mitigates global warming. The success of this technology relies on the advancements of redox materials. Despite the recognition of the entropic effect, usually energy descriptors (enthalpy of formation or energy of oxygen-vacancy formation) were used for computational assessment of material candidates. Here, in the first step, the criteria was derived based on the combination of solid-state change of entropy and formation enthalpy, and was used to thermodynamically assess the viability of material candidates. In the thermodynamic map, a triangular region, featuring large positive solid-state changes of entropy and small enough solid-state changes of formation enthalpy, was found for qualified candidates. Next, a first-principles DFT+U method was presented to fast and reasonably predict the solid-state changes of entropy and formation enthalpy of candidate redox materials, exemplified for pure and Samaria-doped ceria, so that new redox materials can be added to the thermodynamic map. All above results highlight the entropic contributions from polaron-defect vibrational entropy as well as ionic (oxygen vacancies) and electronic (polarons) configurational entropy.