  We predict near-infrared luminosity functions of young (5 Myr to 1 Gyr) star
clusters by combining evolutionary models of very low-mass ($1 M_J$ to $0.15
M_{\odot}$) dwarfs with empirical bolometric corrections. We identify several
characteristic features in our results. These can be attributed to three
causes: (1) deuterium burning in the most massive substellar objects; (2)
methane absorption in bodies with $T_{eff}$ less than 1300 K, the temperature
of the L/T transition; and (3) the formation of dust clouds and the rainout of
dust at roughly the same effective temperature as methane formation. Accurate
reconstruction of the substellar mass function from luminosity function
observations requires that these phenomena are taken into account. At present,
few observational studies extend to sufficient sensitivities to allow detection
of these effects. However, the luminosity function of the young open cluster IC
2391 shows a clear peak at $M_I \sim 14$ which we attribute to the result of
deuterium burning in substellar objects. The location of this feature is a
strong function of age, and we estimate an age of 35 Myr for IC 2391. This is
significantly younger than the 53 Myr derived from the location of the lithium
depletion boundary but agrees with the main sequence turnoff age. We consider
the implications of this result and our multi-band luminosity functions for
future observational studies. All predicted luminosity function features are,
or will be, accessible to observations using new wide-field IR imagers and the
Space Infrared Telescope Facility.
