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There is a ton of data and experimental work on this going back many decades in horticulture because greenhouses want to optimize the conversion of energy to plant growth or crop production. Search on "experiments with DLI and PAR in horticulture" or something along those lines. Sadly, the studies are completely incomprehensible unless one has a sciencey brain. However, it seems likely to me that we aquarists have, by trial and error, found the sweet spot and it is a 6 to 10 hour photoperiod with whatever PAR is needed to mimic the light needs (I think it is the daylight integral) of the plants we grow. Of course, what makes our light needs different from those in a greenhouse monoculture is that we mix plants that evolved at different latitudes in the same tank and those plants have very different light requirements.
