Generalized formulation for ideal light-powered systems through energy and entropy flow analysis Part1. Based on the first-order evaluation

Abstract

In this study, the theoretical maximum efficiency $\eta_{max}$ and the Boltzmann-type factor giving the concentration ratio of excited-to-ground state pigment-molecules for photosynthetic systems under irradiation with arbitrary photon flux density $n_\gamma(\lambda)$, solid angle $\Omega$, and degree of polarization P, are formulated in the most fundamental and general way through energy and entropy flow analysis, using reversibility and the first-order evaluable condition by the photon number change, which is a quasi-equilibrium condition between the radiation and the system, as essential conditions. The radiation temperature for the diluted monochromatic light as non-equilibrium, obtained by the fundamental formulation of this study is found to agree with the conventional radiation temperature, often called the effective temperature, for a given photon flux density (light intensity), provided that $\Omega$ and P of the radiation are 4$\pi$ and 0, respectively. The reason for this agreement is discussed in the final section. The formulation in this study allows quantitative analyses that are not possible with conventional radiation temperature. As examples, the formulation of $\eta_{max}$ taking into account entropy changes due to photochemical reactions such as glucose production by photosynthesis, and various quantities under irradiation at arbitrary $\Omega$ and P are presented. In Appendix C, a specific and rigorous proof, using elementary geometry, of the fact that the entropy of radiation diluted on its way from the Sun to the Earth remains unchanged from its original value, until it is scattered by the Earth's atmosphere, which is guaranteed only in general terms by Liouville's theorem, is given.