Photosynthetic exergy I. Thermodynamic limits for habitable-zone planets

Photosynthesis is central to Earth's biosphere and a prime candidate for sustaining complex life on habitable exoplanets, yet a thermodynamically consistent treatment of the work potential of stellar radiation at planetary surfaces is still lacking. We develop a radiative-thermodynamic framework that quantifies the maximum useful work extractable for a given star-planet configuration and yields exergy-based bounds on photosynthetic power and long-wavelength absorption cutoffs. From these we derive kinetically constrained red limits for high-$\Delta G$ photochemistry and apply them to Earth-like planets receiving the same bolometric flux from FGK and M blackbody hosts, computing thresholded photon supplies and truncated exergy fluxes below a photosystem II red limit. For such planets the constraints confine single-photon oxygenic photosynthesis to near-infrared bands around Solar-type stars and to somewhat bluer wavelengths around late M dwarfs. Integrated over the stellar spectrum, the thresholded photon supply and truncated exergy available to drive a photosystem water-oxidation step are larger by factors $\sim 5$ around FGK hosts than around $T_\star\approx 3000$~K M dwarfs. For the Solar-Earth system, the exergy-based upper bound on O$_2$ production exceeds the observed O$_2$ throughput by several orders of magnitude, consistent with Earth's photosynthetic efficiencies. Cool M dwarfs suffer a double penalty: fewer photons above threshold and a lower shortwave exergy fraction, yielding systematically tighter ceilings on high-$\Delta G$ photosynthesis than around FGK stars. Our framework provides upper limits on photosynthetically harvestable power on habitable-zone planets and enables comparisons of photosynthetic potential across exoplanetary systems, and can be extended to multi-band photosystems.