The Holographic Principle
This is almost correct. If you remember that the Hypergeometrical Universe has one extra non-compact dimension (R) and that the position of each dilator is "ALMOST" perfectly defined by its local dilaton field, one would be tempted to extrapolate this equation into its hyperspatial equivalent.
That would mean that the total information (Entropy) about the particles in a volume of our 3D Hyperspherical Ligthspeed Expanding Universe is contained in the dilaton interferogram on the next de Broglie step. In fact, this is true to a certain point. One cannot forget the ALMOST in the prior statement. An dilaton interferogram will have an infinite number of points spaced with a minimum deviation from the current particle position. At each de Broglie step, the uncertainty on the particle trajectory increases due to non-uniqueness associated with the interferometric process.
If time weren't pseudo-quantized through the Fundamental Dilator Paradigm, the dynamics would be certain and there wouldn't be any quantum mechanics effects.
I suppose that the smaller sign takes care of the interferometric uncertainty (Quantum Mechanics) contribution to the entropy.