One of the interpretation of special relativity states that the time is an illusion and does not really exist. This interpretation promoted Einstein himself in his condolence letter after the death of his friend Michelle Besso(but let's set aside if he actually meant this emotional letter seriously). This interpretation takes into account the determinism that the theory contains. Relativity, contrary to the quantum mechanics, is purely deterministic.
However, I would like to know if there are actually any reasons why to suppose the "nonexistence" of time. Why to chose time from the four dimensions that relativity describes? The theory does not explicitly state we should choose the time dimension to be non-existent, the same can be told about space. Yes, relativity brought to life the problem with definition of simultaneity in time, but the relativity of simultaneity in space is much more trivial and older than the time one.
Also, if we choose to accept that the universe is deterministic and expanding, then the apparent freedom of movement is just as big of an illusion as the one of our perception of time. Because if the universe is deterministic, you have actually no freedom in movement through space - you are predestined to move as you move. If we choose to accept the expansion of the universe, we can also say that we are continuously moving "forwards" in space, let's say from a point our particles were at the moment of the big bang. And probably the point is even out of our reach now thanks to the rapid expansion in the first few moments after the big bang.
Is it only our experience from other fields, like the said thermodynamics, that dictates to choose the interpretation in which we treat time as being "non-existent"? Or are there actual reasons within the relativity itself that the time should be treated as such? Or the apparent empirical observation(irrelevant if time should be an illusion and contradicted in the quantum field theory in which we can interpret antiparticles as particles moving backwards in time and the problem of not enough backwards-time-travelling elements of our world gets transformed into the baryon asymmetry problem) that everything moves forwards in time?