Landauer's bound is an external conditional statement

Landauer's principle concerns physical erasure under specified thermodynamic conditions, not the bare map $B\to \mathsf{I}$ Landauer. Reversible computation and record erasure are distinct tasks Bennett.

For example, the externally established quantum-statistical formulation of Reeb and Wolf starts with an independent memory and a Gibbs reservoir, uses a joint unitary, and defines heat as the reservoir energy increase ReebWolf. With entropy measured in natural units, its Landauer consequence is

under that formulation's hypotheses.

For a uniformly distributed classical bit erased to a fixed pure state, the entropy decrease is $\ln 2$, giving the familiar $k_{\mathrm{B}}T\ln 2$ lower bound. This is not a universal price for every command that discards one syntactic bit:

• a biased or already known bit has a different entropy decrease;

• retained correlations and accessible side information change the resource problem;

• heat and work are not interchangeable without an appropriate Hamiltonian and endpoint specification;

• finite reservoirs, imperfect reset, and attainability have additional restrictions.

The exact reset of a full-rank memory using a finite full-rank thermal reservoir is not presumed available merely because the entropy inequality can be written.

Equation (eq:external-landauer) is a cited external result. No Landauer inequality is derived here from Lemma lem:erasure-interface, Proposition prop:finite, or the source energy identity (eq:energy-source).

Quantum side-information erasure is an established different resource framework delRioEtAl. Its possible work advantages must not be described as violations of a bound whose independent-memory hypotheses no longer hold. No such resource advantage is constructed for the present residual or for the Hawk04-B dynamics.