We develop a simple kinetic model to explain the hysteresis that occur
s when an incandescent light bulb is controlled by a rheostat in the e
xternal circuit. The model is based on changes in the temperature of t
he filament that are associated with internal energy changes due to ra
diation and Joule heating. The radiative processes are idealized as oc
curring via photons lost and gained by a blackbody, while the dynamics
of the electric current are treated via the Langevin equation. Quantu
m corrections to the elementary process description of blackbody radia
tion are derived. Like the ballast resistor, the model exhibits hyster
esis due to a region of bistability of the temperature as a function o
f the resistance in the rheostat, the criterion for stability being th
at the temperature of the filament decreases with increasing resistanc
e in the rheostat, Explicitly including variations in the current, we
show that temperature and current fluctuations are correlated and that
they diverge as the thresholds for stability are approached. It may b
e possible to study these divergences experimentally.