Kolmogorov complexity is not quite the right metric to use, because it doesn’t count the memory usage of the program, just the length of its source code. But the actual cost that’s used to figure out how improbable some configuration is is different. It equals the total number of bits that have to be flipped a certain way, including both the program, the memory it needs to do its job, and any bits that are erased. (The program has to be reversible, so if it has to erase bits, we interpret this as writing those bits to memory that is then not used for anything else.)
Kolmogorov complexity is not quite the right metric to use, because it doesn’t count the memory usage of the program, just the length of its source code. But the actual cost that’s used to figure out how improbable some configuration is is different. It equals the total number of bits that have to be flipped a certain way, including both the program, the memory it needs to do its job, and any bits that are erased. (The program has to be reversible, so if it has to erase bits, we interpret this as writing those bits to memory that is then not used for anything else.)