Merely disagreeing with a guy like Rovelli on physics feels like hubris. :)
But agree with you in this case. Animals perceive the flow of time because we have memory and prediction abilities. This gives us a psychological arrow that aligns with the thermodynamic arrow.
The thermodynamic arrow appears also because we have memory and prediction abilities.
Concepts in statistical mechanics by Arthur Hobson
Publication date 1971
https://archive.org/details/conceptsinstatis0000arth/page/15...
Concerning the concept of time, it is clear that the generalized second law is related in some manner to the question of the "direction" of time. It is sometimes asserted that the second law explains the distinction between past and future, or that the future may be defined as the direction of increasing entropy. This assertion says that the second law is more fundamental than the distinction between past and future.
It seems to the author that the above assertion is wrong. It was seen in Section 5.2 that the generalized second law is derived from the distinction between past and future; hence the distinction between past and future is more fundamental than the second law.
The following statement seems to be the most fundamental physical assertion which can be made regarding past and future: we can classify all instants t into two categories; the first category contains those instants about which experimental data is (or could be) known, and the second category contains those instants about which no experimental data is known. The first category is conventionally called the "past" and the second is called the "future". The instants may be labeled with real numbers running from -∞ to +∞, in such a way that the "past" instants constitute a set of the form (-∞ < t < t0), and the "future" instants constitute the set (t0 < t < +∞). The choice of the positive direction as the future is purely a convention.
According to Sections 5.2 and 5.4, irreversibility and the generalized second law are derivable from the existence of the above two categories of in-stants: an "information-gathering category" (the past), and a "predictive category" (the future). The existence of these two categories seems to be a fundamental feature of nature, not explainable in terms of the second law or in terms of any other physical law.
Well, I am puzzled that Rovelli is not aware about the great debate in modern philosophy about time series A versus time series B that was started in 1908 by a paper on unreality of time by John McTaggart. A consequence of that paper is that perception of the time flow cannot be reduced to a physical process like entropy increase etc. So far nobody was able to disprove that.