If you package bits into a rock at site A and throw the rock, you're converting a bunch of energy from some source into kinetic energy - which ensures that energy being expressed as heat, defeating your purpose. In fact, I'm pretty sure you're guaranteed not to break even on this.

The bits you're packaging into the rock make the rock heavier (bits are entropy, entropy is energy, E=mc^2) establishing a lowerbound on the mass required to contain them. That gives you a mass density per volume dependent on the speed with which the mass moves, putting a lowerbound on the (radiating) energy required to accelerate the mass - and it turns out that you're generating heat at the source at least equal to the heat you're "displacing" to a remote site. Same basic argument as Maxwell's Demon.

The bits you're packaging into the rock make the rock heavier (bits are entropy, entropy is energy, E=mc^2) establishing a lowerbound on the mass required to contain them. That gives you a mass density per volume dependent on the speed with which the mass moves, putting a lowerbound on the (radiating) energy required to accelerate the mass - and it turns out that you're generating heat at the source at least equal to the heat you're "displacing" to a remote site. Same basic argument as Maxwell's Demon.