Has the connection been noted between these two? I have been studying special relativity and in learning Minkowski diagrams I have noticed that as v approaches c, the relativity of simultaneity is so drastic that all of what any observer would call effects happen simultaneously with their causes. In other words, entropy can't be said to increase for that observer. This relationship between the relativity of simultaneity and entropy holds for all other velocities as well and after a little thought it seems obvious: time dilation occurs occurs with the relativity of simultaneity because a change in the order of events (rel of sim) is a change in the increase of entropy (second law of thermodynamics) for any observer, which defines the arrow of time. If entropy increases as events occur for any frame of reference, then if that frame experiences the relativistic effects of changes in the ordering of events, they will experience time dilation due to a lessening of entropy's increase (to the the extent of the relativistic effects of reordering of events). The relativity of simultaneity must cause time dilation due to the definition of the arrow of time in thermodynamics. I would like to express this mathematically, though I am just learning the math of relativity now. I am curious as to why I have not seen this point made yet. I can hardly imagine this connection would not be seen as interesting enough for anyone to mention in teaching these two fundamental ideas...?
Edit: because the question/idea has seemed unclear to many people I will state it like this. I believe there is a deep equivalence between relativity and thermodynamics. Viewing our universe as a system evolving toward higher entropy with time, I believe that any perspective which experiences less time (time dilation) must do so because they experience less entropy. Because entropy is defined by the most probable statistical evolution of events, an inertial frame which experiences time dilation (less entropy) must experience a less probable ordering of events, which happens via the relativity of simultaneity. Note that the probability of experiencing an increasingly highly relativistic perspective (for instance, from random natural accelerations) is increasingly rare exactly because it takes energy to do so, exactly as it is increasingly rare to find thermodynamic systems evolving toward states further and further from maximum entropy. I am not saying anything about violating causality, simply that (referring to thermodynamics) there are evolutions which at times momentarily shift away from maximum entropy, but don't violate the second law because they don't decrease entropy, just as there are relativistic frames that experience an ordering of events from the relativity of simultaneity that slow but do not reverse time.