Sean Carroll is always interesting on the connection between entropy and the arrow of time. However, like all believers in block universe/eternalist-type theories he does not provide an adequate explanation for why there is a subjective experience of the flow of time or why there is a moment called “now” which is somehow special. Under a non-eternalist view time has an arrow and entropy increases along that arrow but does not cause it. With all that said his “From Eternity to Here” is one of the most mind-expanding books I’ve ever read.
The challenge here for me is that all the best philosophical arguments support the A-series (tensed) theory of time while all the best scientific ones support the B-series (tenseless). But the scientific “arguments” here are just plausible science-sounding explanations, not actual testable theories that could refute once and for all the notion that time is tensed. Further, the strongest empirical evidence (direct sensory perception) seems to support the A-series; attempts to deny this sound like the weak attempts to deny the existence of qualia (which are real because you perceive them and which need no further justification). Lee Smolin appears to have come out in favor of the A-series from a scientific point of view but I have not yet read his new book “Time Reborn.”