So it seems if it would be possible to have/process information without energy those limits would be infinite. At least my layman reasoning leads me to believe this.
"<...>a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately 1075 mathematical computations per second.<...>"
Yeah, right, it's a number so large on a human scale that it's essentially incomprehensible. However, if you think about it for a moment you can begin to imagine the enormity of the complexity. Leaving aside how you'd calculate said figure or dream about how it could ever be implemented, just try to consider the humongous amount of information that's contained in just one gain of sand.
One must account for the amount of information contained within the configuration or quantum state of the trillions upon trillions of atoms and molecules along with all their constituent particles, electrons, protons, quarks—all of which contain information that's arisen from the quantum states of the various binding forces—the state of electromagnetic, strong and weak forces.
Then there's information generated by the couplings and various physical characteristics of all the crystal lattices including all geometric information contained in each crystal's facets to be considered, not to mention various charges/interconnecting effects involved with crystal binding such as van der Waals forces and other quantum effects/fluctuations. Then we've also to consider all information generated from the sand grain's thermodynamic state (and that alone would be enormous).
And that's not all, even information from phonon movement (noise) generated from within each crystal as well all noise coupled from external sources must be included. Vibrational/phonon energy, which in the real world is lossy, generates information from its dissipated thermal energy (even information is generated from the physical state/properties of matter that actually cause those losses).
Thus, the total amount of information in just one grain of sand alone is simply mind-boggling.
Now extrapolate all that to all those other grains of sand until we get to earth-size. And now also take into account the fact that when all those many grains are closely packed together, they generate even more information by virtue of their couplings (van der Waals forces now act between individual grains of sand, and so on and so on).
'Mind-boggling' doesn't come even close to describing the informational complexity!
So it seems if it would be possible to have/process information without energy those limits would be infinite. At least my layman reasoning leads me to believe this.