  I apply the thermodynamics of radiation to Dyson spheres as machines that do
work or computation, and examine their observational consequences. I identify
four properties of Dyson spheres that complicate typical analyses: globally,
they may do no work in the usual sense; they use radiation as the source and
sink of energy; they accept radiation from a limited range of solid angle; and
they conserve energy flux globally. I consider three kinds of activities:
computation at the Landauer limit; dissipative activities, in which the energy
of a sphere's activities cascades into waste heat, as for a biosphere; and
"traditional" work that leaves the sphere, such as radio emission. I apply the
Landsberg formalism to derive efficiency limits in all 3 cases, and show that
optical circulators provide an "existence proof" that greatly simplifies the
problem and allows the Landsberg limit to be plausibly approached. I find that
for computation and traditional work, there is little to no advantage to
nesting shells (as in a "Matrioshka Brain"); that the optimal use of mass is
generally to make very small and hot Dyson spheres; that for "complete" Dyson
spheres we expect optical depths of several; and that in all cases the
Landsberg limit corresponds to a form of the Carnot limit. I explore how these
conclusions might change in the face of complications such as the sphere having
practical efficiencies below the Landsberg limit (using the endoreversible
limit as an example); no use of optical circulators; and swarms of materials
instead of shells.
