Landauer’s principle states that in erasing one bit of information, on average, at least $k_{B}T\ln \mathrm{}\left(2\right)\mathrm{}$ energy is dissipated into the environment (where $k_B$ is Boltzmann’s constant and $T$ is the temperature of the environment at which one erases). Here, Landauer’s principle is microscopically derived without direct reference to the second law of thermodynamics. This is done for a classical system with continuous space and time, with discrete space and time, and for a quantum system. The assumption made in all three cases is that during erasure the bit is in contact with a thermal reservoir.

• Received 27 September 1999

DOI:https://doi.org/10.1103/PhysRevA.61.062314