Three ledgers and thermodynamic underdetermination

This reproduces the separation illustrated in the supplied En07-A record by a local counterexample, rather than treating that record as a premise CheungEn07A.

external thermal inequality. In the specified thermal setting of an initially uncorrelated memory and Gibbs reservoir undergoing complete unitary evolution, the reservoir heat satisfies

with entropy in natural logarithms. A decrease of one unbiased classical bit corresponds to $Q_{\mathrm{bath}}\ge k_{\mathrm{B}}T\ln 2$. These statements belong to the additional thermal setup, not to the equality $\mathsf{Drop}\circ \mathsf{Enter}={\mathrm{Tr}}_B$ Landauer1961,ReebWolf. Finite reservoir effects, reset accuracy, correlations, and consumed resources require their own accounting.

No thermal machine implementing the present Enter interface has been constructed. The implementation package required for a successor is listed in Appendix app:thermal.