Christian is without a doubt a historian through and through, and is quite upfront about his general lack of scientific expertise and background. He has however spent quite a bit of time working with and consulting physicists, chemists, biologists, and other scientists to supplement the appropriate portions of his bigger thesis. I would say though, that he's got firm footing in both of C.P. Snow's "Two Cultures."
Christian references Prigogine only once, though includes two Prigogine related footnotes in the last quarter of the text. He's not as Prigogine-centric as [author:César Hidalgo|13831217] is in his recent [book:Why Information Grows: The Evolution of Order, from Atoms to Economies|25472587], which touches on some of the related physics of information theory and entropy (and general complexity theory - although I don't recall him using this specific term) as they relate to economics. I'd classify Why Information Grows as a "big history" book, though Hidalgo wasn't aware of the conceptualization of "big history" when he wrote it.
I wrote a slightly longer review of Christian's book(s) on my blog: http:/