@RexKerr, there are multiple. One is "wavefunction collapse" (if that happens). Another is quantum fluctuations. Another would be general uncertainty or according to a better German -> English translation, the "unsharpness relation". Another would be stochastic decay of particles. I'm not sure if I'm missing any.

@labreuer - Just as there's room within physicalism to admit randomness, there's room for it to be found unnecessary again.

If stochastic decay occurs at measurably non-random times, or is affected by external processes, then we have to revise our theories regarding it.

If those external processes are conceptually simple but mechanistically complex with no connection (e.g. the prayers of all North Americans), then physicalism is in really big trouble.

If those external processes are equally simple and we just didn't notice it before--for example, a stronger dependency on space-time curvature than thought but which makes sense with a theory of gravitation better integrated with indeterminacy--then physicalism is fine and we just slot in the new theory.

And if there's no causal chain of necessity, if it's just some random process like we think, then that's fine for physicalism too.

So I don't really see how things we don't know that involve e.g. probability distributions rather than individual outcomes are any different in kind than things we don't know that involve individual outcomes. Unexpectedly energetic gamma rays aren't cause to doubt physicalism, are they? But we see them.