Earlier quoted context omitted.
> This doesn't take into account that you will inevitably want to assign unique IDs to various groups of atoms (e.g. this microchip, that car, etc.). Sure it does. Those are not going to add up to a single extra bit.
Even every possible permutation of every single subatomic element in the universe? Even if we just consider atoms, at 10^80 atoms in the entire universe, there are (10^80)! possible permutations, which is many, many, many orders of magnitude larger. And this isn't even counting sets that include multiples of the same item; once you get into that territory, there really is no upper bound.
Definitely no multiples. What would that even mean, also you would need unbounded space for multiples of just two atoms.