For example, when talking about the second law of thermodynamics and entropy, he claims (I think - it's difficult to tell exactly what he is claiming) that the only reason we perceive the arrow of time from the increase of entropy is the way we label things.

The wofflyness often gets in the way of understanding. At one point he speaks of a world without time, elsewhere he says 'Time and space are real phenomena.' The difficulty I think Rovelli faces is that he uses the common physicist's approach of talking of a model as if it were reality. For example, at one point within a page of telling us of time's absence Rovelli writes of events that have duration and a 'when' - both meaningless terms without time. Time and again (pun intended) he tells us time doesn't exist, then makes use of it. It doesn't help either that the book is in translation so some scientific terms are mangled, or that Rovelli has a habit of self-contradiction. The bad news is that Carlo Rovelli does this in such a flowery and hand-waving fashion that, though the reader may get a brief feeling that they understand what he's writing about, any understanding rapidly disappears like the scent of a passing flower (the style is catching).

The good news is that The Order of Time does what A Brief History of Time seemed to promise but didn't cover: it attempts to explore what time itself is.

The Order of Time by Carlo Rovelli