  We introduce information-theoretic erasure based on Shannon's binary channel
formula. It is pointed out that this type of erasure is a natural
energy-dissipation-free way in which information is lost in
double-potential-well memories, and it may be the reason why the brain can
forget things effortlessly. We also demonstrate a new non-volatile,
charge-based memory scheme wherein the erasure can be associated with even
negative energy dissipation; this implies that the memory's environment is
cooled during information erasure and contradicts Landauer's principle of
erasure dissipation. On the other hand, writing new information into the memory
always requires positive energy dissipation in our schemes. Finally, we show a
simple system where even a classical erasure process yields negative energy
dissipation of arbitrarily large energy.
