The duration-luminosity phase space (DLPS) 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 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 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 ( 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 days are dim ( mag). Finally, we explore the detection potential of optical surveys (e.g., Large Synoptic Survey Telescope) in the DLPS and quantify the notion that short-duration and dim transients are exponentially more difficult to discover in untargeted surveys.