  Time-dependent protocols that perform irreversible logical operations, such
as memory erasure, cost work and produce heat, placing bounds on the efficiency
of computers. Here we use a prototypical computer model of a physical memory to
show that it is possible to learn feedback-control protocols to do fast memory
erasure without input of work or production of heat. These protocols, which are
enacted by a neural-network ``demon'', do not violate the second law of
thermodynamics because the demon generates more heat than the memory absorbs.
The result is a form of nonlocal heat exchange in which one computation is
rendered energetically favorable while a compensating one produces heat
elsewhere, a tactic that could be used to rationally design the flow of energy
within a computer.
