Kinetic theory, thermodynamics and hence entropy is a fundamental property of ANY universe consisting of a large number of independent particles interacting under ANY sort of physical(or chemical ) laws and is totally independent of its starting conditions.

I agree entropy can still be defined, independent of the special initial conditions, but it's not such an interesting quantity in that case.

Let me explain why I say that. The point is that the increase of entropy can only come about if the entropy starts off low. For instance, two different gases released separately into a box will mix together, and that represents an increase in entropy. But if you start out with the gases mixed in the first place, there's no way for the entropy to increase any further.

On a closer inspection of this, Boltzmann realized that entropy could decrease if you wait for an immensely long time. However basic modern cosmology doesn't have that picture: it assumes the universe somehow started out in the low entropy state.

Inflation is (according to its more thoughtful proponents) a mechanism for generating a low entropy Universe in a way consistent with Boltzmann's view; in that sense the real 'initial conditions' are supposed not to matter so much, because they are hidden away from us by the inflationary epoch. (However these issues are

*very* complex and still far from cleared up.)

The really vital asymmetries that would drive it are gravitation

Gravity's actually time-symmetric. The asymmetry comes from the fact that things don't start off in a gravitationally collapsed state (i.e. they start off smoothly spread out, not in black holes).

and quantum uncertainty

You're right that quantum mechanics generates its own arrow of time (in the conventional formulation), and the agreement between the entropy-derived arrow of time and the QM-derived arrow of time is then a rather odd coincidence. My personal view is that this is an illusory, and a fuller understanding of quantum mechanics will show us that the thermodynamic and quantum arrows of time have to be the same. (This is rather beautifully the case in, for instance,

Everett's picture of quantum mechanics.)

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