of each summation in Eq. (8): in order to minimize ΔG, they must be as negative as possible: : -ΔS°i are negative, so (T-T°) must be as high as possible: hence, one choose to operate at the maximum process temperature TH : -ΔS°i are positive, (T-T°) should be ideally negative in order to decrease ΔG. Practically, one can only set T equals to T° as the minimum process temperature in order to get rid of this troublesome term (a process requiring a lower than standard temperature for energy production is a physical absurdity as it would require refrigerators and thus a higher work input than output). Consequently, Eq.(8) becomes, (9) Finally, one can deduce from this last equation the relationship required for a null work requirement (ΔG ≤ 0) (10) Consequently, a thermochemical cycle with i steps can be defined as sequence of i reactions equivalent to water-splitting and satisfying equations (4), (5) and (10). The key point to remember in that case is that the process temperature TH can theoretically be arbitrary chosen (1000K as a reference in most of the past studies, for high temperature nuclear reactors), far below the water thermolysis one. This equation can alternatively (and naturally) be derived via the Carnot's theorem, that must be respected by the system composed of a thermochemical process coupled with a work producing unit (chemical species are thus in a closed loop): at least two heat sources of different temperatures are required for cyclical operation, otherwise perpetual motion would be possible. This is trivial in the case of thermolysis, as the fuel is consumed via an inverse reaction. Consequently, if there is only one temperature (the thermolysis one), maximum work recovery in a fuel cell is equal to the opposite of the Gibbs free energy of the water-splitting reaction at the same temperature, i.e. null by definition of the thermolysis. Or differently said, a fuel is defined by its instability, so if the water/hydrogen/oxygen system only exists as hydrogen and oxygen (equilibrium state), combustion (engine) or use in a fuel cell would not be possible. endothermic reactions are chosen with positive entropy changes in order to be favored when the temperature increases, and the opposite for the exothermic reactions. maximal heat-to-work efficiency is the one of a Carnot heat engine with the same process conditions, i.e. a hot heat source at TH and a cold one at T°, (11)