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.