I don't think it's inaccurate to regard a "process" as merely a sequence of causally-connected events, though. That notion covers the sorts of things that biological organisms do, to be sure, but it also opens up the field to a whole host of things that have nothing to do with biology - I think it's entirely accurate and fair to describe a volcanic eruption as a "process", so what we're going to end up doing is discussing where life begins and ends, probably.
I'd say fire is too simple to be considered alive. Similarly prions and an automobile assembly line.
Based on what? Complexity? The number of discrete processes that happen to occur comtemporaneously? My CPU has more transistors than IBM has employees - is it alive, based solely on its complexity?
Well, yes of course - that was my original point. I'd say if there is an isomorphism (of some reasonably high level of precision) between system S1 performing process P1 to another system S2 doing process P2 and we classify S1 as alive then S2 should also be so classified. It is the structure that is important.
it's entirely accurate and fair to describe a volcanic eruption as a "process",
Again yes, but it is a very simple process. Not much more complex really than the hydrologic cycle.
My CPU has more transistors than IBM has employees - is it alive, based solely on its complexity?
100,000,000 transistors all the same isn't complex. Granted that's an exaggeration (they're not all the same) but not a large one. The CPU would fail other criteria too. For example, it can't process without an environment of complexity similar to itself while living things maintain themselves by metabolizing simple inputs.