Yes, but only briefly. When you study the thermodynamics of information you’ll discover that it’s actually erasing information that has a cost. Every time the CPU stores a value in a register it erases the previous value, using up energy. In fact, every individual transistor has to erase the previous state on basically every clock cycle.
Curiously there is a minimum cost to erase a single bit that no system can go below. It’s extremely small, billions of times smaller than the amount of energy our CPUs use every time they erase a bit, but it exists. Look up Landauer’s Limit. There is a similar limit on the maximum amount of information stored in a system which is proportional to the surface area of the sphere that the information fits inside. Exceed that limit and you’ll form a black hole. We’re no where near that limit yet either.
