I would start by saying, just to clarify slightly, that I think that speaking of logical causation is misleading, as (it is explained by other answers) "because" is not a truth operator. (Hence logical necessity works better.)
Wittgenstein famously states that (Tractatus Logico Philosophicus, proposition 5.1361) : "The events of the future cannot be inferred from those of the present." and "Superstition is the belief in the causal nexus."
Later (Propositions 6.37, 6.371 and 6.362) "A necessity for one thing to happen because another has happened does not exist. There is only logical necessity. At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena. So people stop short at natural laws as at something unassailable, as did the ancients at God and Fate. And they both are right and wrong. But the ancients were clearer, in so far as they recognized one clear conclusion, whereas in the modern system it should appear as though everything were explained."
A Wittgensteinian answer to this question would that there is no such thing as physical causation as is generally understood in modern science, but that physical causation is an a priori intuition, which is useful for hypotheses, but which tells us nothing about the world in-itself or its meaning.
I would also like to add what I perceive to be a flaw in the positivist approach of science and philosophy, which is the one which seems to lead most physicalists to their position and its implications, about causation, determinism, etc...
When the positivist declares that all valuable knowledge comes from science (or broadly, some application of the scientific method), this assertion is scientifically unjustifiable.
There is no "science of the sciences" from which to draw conclusions, and we can see that the justifications of the positivist position rest on other types of affirmations, notably such as priori intuitions, but also beliefs, values, etc...
Despite the rhetorical appeal of Carnap's (one of the historical spearheads of positivism) claim that "Metaphysicians are musicians without musical talent", one would resolutely qualify it of unscientific.