Planetary atmosphere are entropy pumps. The surface of a atmosphere-clad planet is out of thermodynamic equilibrium, providing an inversion of available free energy, in the same way that a laser works through pumping a population inversion of metastable states. Life can be approximated as a classical refrigerator, using the locally available disequilibrium to pump out excess entropy.
Brains, too, it turns out, are entropy pumps, also creating a disequilibrium that can be exploited. Any calculation–any thought–is also a miniature refrigerator, locally lowering the entropy through differences in the local free energy.
From this one can not only estimate the biomass any planet can support, but also the “noomass” of intelligence it can support. This being a fairly straightforward application of the Carnot cycle, I leave it to the reader to work out.
Alas, the numbers confirm that we exceeded the planetary limit somewhere in 1971. While local pockets of entropy can continue to decrease, we literally have no more intelligence to hand out.