So tell me, Professor, does Boltzmann's equation have a material cause? How about natural logarithms -- are they the product of matter in its modifications/motions? Or the British taste for luke-warm beer for that matter? Or the fact that I like mine icy cold?
Personally, I don't think Penrose's probability calculation is at all specious.
No. It's, in effect, a molecular statement of the Second Law. It's a feature of the Universe as we observe it.