Universal entropic occupation statistics in disordered bosonic resonators

Abstract

Programmable microcavities support grand-canonical photon gases. We show that bosonic state counting creates an entropic staircase of most-probable total occupations. For detuning density continuous and nonzero at the chemical-potential threshold, the active-cell fraction is asymptotically linear at low temperature and the conditional law has a universal limit; for uniform disorder the law is exact over a finite temperature interval. For two modes it is the Gauss--Kuzmin distribution, linking photonic thermodynamics and metric number theory. We outline finite-array and dye-microcavity tests.