> In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level.[1] It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science, this implies that there is a maximal information-processing rate (Bremermann's limit) for a physical system that has a finite size and energy, and that a Turing machine with finite physical dimensions and unbounded memory is not physically possible.
Lots of math works out well that as a continuous approximation, eg the Navier-Stokes differential equations seem to describe fluids well on everyday scales. But we know very well that water is made of molecules, so we know that this particular continuous approximation will fail at small enough scales.
By the way, the closest thing we have come to for teleportation is cutting-and-pasting of quantum states. So no classical, digital computers involved there.
You might be interested in the Bekenstein bound (https://en.wikipedia.org/wiki/Bekenstein_bound):
> In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level.[1] It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science, this implies that there is a maximal information-processing rate (Bremermann's limit) for a physical system that has a finite size and energy, and that a Turing machine with finite physical dimensions and unbounded memory is not physically possible.
Lots of math works out well that as a continuous approximation, eg the Navier-Stokes differential equations seem to describe fluids well on everyday scales. But we know very well that water is made of molecules, so we know that this particular continuous approximation will fail at small enough scales.
By the way, the closest thing we have come to for teleportation is cutting-and-pasting of quantum states. So no classical, digital computers involved there.