The Landauer Limit

Landauer's principle is the proof that every act of forgetting costs energy. Specifically: any logically irreversible computation—the paradigm case being the erasure of a memory register, which maps two distinguishable prior states (zero or one) onto one final state (zero)—must dissipate at least kT ln 2 joules of heat per bit erased, where k is Boltzmann's constant and T is the temperature of the surrounding environment. At room temperature this is roughly three zeptajoules—an inconceivably small number. Today's processors waste energy at a rate billions of times above this floor, burning heat through resistance and leakage long before the fundamental limit matters. But the floor is real, and it has entered engineering relevance as frontier AI systems consume electricity at the scale of small cities: every training run, every inference, every attention operation that selects some information and discards the rest is paying above the Landauer minimum for every bit erased.