  The Chern index characterizes the topological phases of nonreciprocal
photonic systems. Unlike in electronic systems, the photonic Chern number has
no clear physical meaning, except that it determines the net number of
unidirectional edge states supported by an interface with a trivial mirror.
Here, we fill in this gap by demonstrating that the photonic Chern number can
be understood as a quantum of the light-angular momentum in a photonic
insulator cavity. It is proven that for a large cavity, when the discrete
spectrum can be approximated by a continuum, the spectral density of the
thermal fluctuation-induced angular momentum is precisely quantized in the
band-gaps of the bulk states. The nontrivial expectation of the light angular
momentum is due to a circulation of thermal energy in closed orbits.
Remarkably, this result can be extended to systems without a topological
classification, and in such a case the "quantum" of the angular momentum
density is determined by the net number of unidirectional edge states supported
by the cavity walls.
