Landauer's principle

A classical bit that may be either 0 or 1 with equal probability has one bit of Shannon entropy. Resetting it to a definite value, such as 0, removes that uncertainty. Landauer's principle states that when this logical erasure is performed in contact with a heat bath at temperature T, the minimum work required in the ideal, quasistatic limit is kBT ln 2, where kB is Boltzmann's constant. In an isothermal erasure cycle, at least this amount of heat is released to the bath. At room temperature the energy is extremely small, but the principle is a thermodynamic lower bound, not a prediction of the energy used by ordinary computers, which dissipate far more.

The principle concerns operations whose outputs do not uniquely identify their inputs. Erasing either 0 or 1 to the same output is a simple example; so is merging distinct computational paths. Such a many-to-one mapping discards information about the prior state. By contrast, a logically reversible operation maps each allowed input to a unique output and can, in principle, be carried out with arbitrarily small dissipation if performed sufficiently slowly under suitable conditions. Real devices face practical costs from speed, noise, resistance, error correction and other design constraints, none of which are set equal to the Landauer bound.

Computations often generate temporary data that is later reset to make memory available again. This reset step is where the Landauer cost is directly relevant. Charles Bennett's analysis of reversible computation showed how a deterministic computation can, in principle, be reformulated as reversible steps, retaining or uncomputing intermediate data rather than erasing it as it goes. This does not make practical computing energy-free: hardware still dissipates energy, and eventually disposing of unwanted information can incur a thermodynamic cost. The distinction is between the unavoidable ideal cost of erasure and the typically much larger engineering costs of a real device.

In 2012, Antoine Bérut and colleagues reported an experimental test using a single colloidal particle in a modulated double-well potential as a one-bit memory. The two wells represented the two states. By controlling the potential, the researchers erased the bit and measured dissipated heat. For long erasure cycles, the mean dissipated heat approached the Landauer bound, providing an experimental demonstration of the predicted limit in this model system. The result tests erasure under controlled laboratory conditions; it does not imply that all operations in computers dissipate precisely kBT ln 2 per bit.

The simple kBT ln 2 expression assumes an initially unknown, equiprobable bit and an isothermal process with a thermal reservoir at temperature T. If the initial probabilities are unequal, the relevant information entropy differs, and the minimum work depends on the change in entropy under the chosen physical model. More generally, information may be stored in physical degrees of freedom, so claims about the cost of an operation depend on how the memory and environment are defined. The principle is a central result in the thermodynamics of information, though its interpretation and foundations have also been the subject of scholarly debate.