Consistent with special relativity and statistical physics, here we construct a partition function of space-time events. The union of these two theories resolves longstanding problems in regards to time. It augments the standard description of time given by the (non-relativistic) arrow of time to one able to show the emergence of three macroscopic regimes of time: the past, the present, and the future, represented by space-like entropy, light-like entropy, and time-like entropy, respectively, and in a manner consistent with our experience of said regimes. First, using Fermi-Dirac statistics, we find that the system essentially describes a "waterfall" of space-time events. This "waterfall" recedes in space-time at the speed of light towards the direction of the future as it "floods" local space with events that it depletes from the past. In this union, an observer O will perceive two horizons that can be interpreted as hiding events behind it. The first is an event horizon, and its entropy hides events in the regions that O cannot see. The second is a time horizon, and its entropy "shields" events from O's causal influence. As only past events are "shielded", and not future events, an asymmetry in time is thus created. Finally, future events are hidden by an entropy prohibiting O from knowing the future before the present catches on.
The Quaternion Structure of Space-Time and Arrow of Time