  The duration-luminosity phase space of optical transients is used, mostly
heuristically, to compare various classes of transient events, to explore the
origin of new transients, and to influence optical survey observing strategies.
For example, several observational searches have been guided by intriguing
voids and gaps in this phase space. However we should ask: Do we expect to find
transients in these voids given our understanding of the various heating
sources operating in astrophysical transients? In this work, we explore a broad
range of theoretical models and empirical relations to generate optical light
curves and to populate the duration-luminosity phase space (DLPS). We explore
transients powered by adiabatic expansion, radioactive decay, magnetar
spin-down, and circumstellar interaction. For each heating source, we provide a
concise summary of the basic physical processes, a physically motivated choice
of model parameter ranges, an overall summary of the resulting light curves and
their the occupied range in the DLPS, and how the various model input
parameters affect the light curves. We specifically explore the key voids
discussed in the literature: the intermediate luminosity gap between classical
novae and supernovae, and short-duration transients (<10 days). We find that
few physical models lead to transients that occupy these voids. Moreover, we
find that only relativistic expansion can produce fast and luminous transients,
while for all other heating sources, events with durations <10 days are dim (>
-15 mag). Finally, we explore the detection potential of optical surveys (e.g.,
LSST) in the DLPS and quantify the notion that short-duration and dim
transients are exponentially more difficult to discover in untargeted surveys.
