Some phenomenons suggest an arrow of time that are not (or loosely) related to thermodynamics and the 2nd law.
Take one of the most basic way humanity measured time, the cycle of the sun in the sky. What makes the sun go from east to west in a regular motion whose period we call a day? It's the momentum of Earth's rotation, which is always conserved according to Newton's laws of motion.
It can often be seen that "in Newtonian physics time can be reversed", but this is just a property of the model, not reality. Although it is true that in Newton's equations a negative time value can be plugged, it is never observed in reality that moving object reverse course or change velocity on their own, because their momentum is conserved at all time. Now that it is set on its path, Earth's motion around the sun can only happen in one direction, unless tremendous force is applied to it. This has nothing to do with thermodynamics and yet is the reason astronomical bodies' motion is so regular, and have been humanity's first way to keep track of time.
There are forces that apply only in one direction, like gravity. Objects fall, but never climb up on their own. That's one of the reason why, if we see a footage of a splashed egg on the ground reforming and jumping back into a cook's hand, we instinctively know it has been reversed, because gravity acts only one way, which is down. Again, this is not linked to thermodynamics.
There is also the notion of information and the loss thereof. Here by information I mean the relationship of parts of an object inside of it, the structure of the object. This is what makes the difference between a random ink spot on a paper and the same amount of ink used on the same paper to write a note: the amount and elements of atoms are the same in both, but the way they are disposed makes the difference.
In some events, this information is lost. Take the aforementioned drop of an egg: once the egg is broken, the information about its shape, which was contained in the egg itself, is lost forever. That is why it can be broken only once, with a clear distinction with before and after it was broken. Although this might be related to Boltzmann entropy (which I am not familiar with), this is not related to thermodynamics (the amount of heat exchanged in a egg breaking is negligible).
So although the fact that heat can transfer only from a hot source to a colder recipient is one example of irreversible phenomenon, we can see that momentum, the application of forces and the loss of information, none of which are related to thermodynamics, are also an illustration of the concept of time and why it flows only in one direction.