Landauer's principle intuitively: the laws of physics are reversible, and therefore two distinct states (1 or 0) always map to two distinct states (1 or 0, evolved). So how can you erase a bit - take a 1 or 0 and map them to a 0? The answer is that you have to send the 0 or 1 to the environment i.e. map 1 or 0 to (system,environment) = (0,1) or (0,0) , which manifests as the dissipation of heat.
So where does the information go upon the final heath death of the universe? Does it become encoded by, say, the final diameter of the post-expansion universe (i.e. by some "environmental" property at the sub-quantum field level)?
The information doesn’t go anywhere. In the heat death of the universe all particles are at absolute zero due to the heat of the universe spreading uniformly in the vacuum of space.
