The Quest for the Ultimate Theory of Time: Physical Stability or Empty Probability?

The question of the direction of time, or the arrow of time, is still haunting physicists with the physicist and cosmologist Sean Carrol expressing state of art in e.g. the book From Eternity to Here: The Quest for the Ultimate Theory of Time, which is basically to say following old Boltzmann: There is a quantity named entropy, which cannot decrease with time and when strictly increasing sets a direction of time motivated by Carroll as follows in an introduction:

• The reason why entropy wants to increase is deceptively simple:
• There are more ways to be disorderly than orderly, so an orderly arrangement will naturally tend toward increasing disorder.

But Carroll is not very happy with this his explanation:

• If everything in the universe evolves toward increasing disorder, it must have started out in an exquisitely ordered arrangeement...a state of very low entropy.
• Why were conditions in the early universe set up in a very particular way? That is the question this book sets out to address.
• Unfortunately, no one yet knows the right answer.

And then follows the rest of the book, without answer. The only attempt to give reason to the tendency of entropy to increase, is to argue following Boltzmann, that things naturally evolve from less probable/low entropy states to more probable/higher entropy states. But of course this is circular: To say that more probable is more probable than less probable is a tautology without actual content.

In the book The Clock and the Arrow: A Brief Theory of Time I argue that there is another way of explaining the arrow of time and that is with reference to the physics of stability instead of the non-physics of probability of Boltzmann. The key point is:

• A system cannot remain in an unstable state because the inevitable effect of small fluctuations will have a major effect and thus transform the system to either a more stable state of more or less rest or to another unstable state of non-rest. 
• The transition from unstable to stable rest is irreversible since the reverse process from stable rest to unstable is impossible without major exterior forcing. 
• The transition from unstable is sensitive to small perturbations along with the formally reversed process, and thus cannot be reversed under any form of finite precision physics.    

Here is a summary of my view and that of Boltzmann/Carroll:

1. An arrow of time is given by physical stability properties of certain systems making them irreversible, without asking any specific order of an early universe.
2. An arrow of time is motivated by an empty tautology stating that systems evolve from less probable to more probable states, asking for a highly improbable highly ordered early universe. 

You may decide yourself between 1. and 2. Which is more probable?