Halliday & Matthiessen (1999: 133-4):
The complementarity can also be seen in the different kinds of deixis (relation to the here & now) associated with processes on the one hand and participants on the other. A process is made finite — it is pinned down in time, with point of reference in the act of speaking. A participant is made determinate, being held in a location within a referential space. This same distinction also appears in the temporal unfolding of a text, where participants have the potential to persist as discourse referents, but processes are excluded, unless they are turned into honorary participants through the use of grammatical metaphor.