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Certain questions regarding the analysis of theoretical maximum energyefficiency $\eta_{max}$ of light-powered systems by the radiant temperature andits use for the Boltzmann coefficient remain unanswered. A potential reason forthis could be the confusion about equilibrium and reversibility. Therefore,this study performed a quantum statistical entropy analysis of a light-poweredsystem based on reversibility as the solely essential condition and withoutrecourse to the concept of radiation temperature. Several quantitative analysesthat cannot be performed with radiation temperature can be performed using thegeneralized formula. As examples, this study presents the formulation of$\eta_{max}$ considering the entropy change caused by photochemical reactions,such as that in photosynthesis and photosynthetically active radiation (PAR),and the formulations of several quantities under radiation with arbitrary$\Omega$ and P. Furthermore, analysis from this study found that $\eta_{max}$decreases as the light absorption rate increases, which had not previously beenconsidered. This general formula is presented, which fills the gap between theJeter efficiency (Carnot efficiency) $\eta_{C}=1-T_{out}/T_{in}$ and theSpanner efficiency $\eta_{S}$=1-(4/3)$T_{out}$/$T_{in}$ (where $T_{out}$ isambient temperature and $T_{in}$ is the temperature in the system) forblack-body radiation. The analyses generally formulated in this study allowpractical analyses of systems such as photosynthesis and photovoltaics, undervarious conditions relating to sunlight scattered through the atmosphere.  Finally, it is proved with elementary geometry that the total entropy of thesolar radiation from the Sun to the upper atmosphere of the Earth remains at aconstant value. This means that the use of solar energy on satellites in spaceis expected to be more efficient than on the earth's surface.

Generalized formulation of theoretical maximum energy efficiency of light-powered systems based on photon entropy analysis