Is our theoretical data storage size and processing bounded by physical laws? I would assume computation is, but is information storage limited by entropy or the physical volume of the universe?
The information you can store in a given region of space is constrained by the working together of two fundamental laws of physics:
Heisenberg's uncertainty principle (HUP) (i.e. the size of Planck's constant h)
Einstein's general relativity (GR) (i.e. the strength of Newton's gravitational constant G)
In order to pack more and more information in a given volume you need to probe smaller and smaller distance scales. But HUP implies this requires using more and more energy.
GR though implies more energy means more mass, and so at some point the volume will collapse into a black hole. So what you may ask: the trouble is that black hole dynamics demands that as you pump more energy into a black hole it will just get bigger. There is no physical way of pumping any more energy into the region whilst keeping that region at a fixed volume.