The (absence of a) relationship between thermodynamic and logical reversibility

Landauer erasure seems to provide a powerful link between thermodynamics and information processing (logical computation). The only logical operations that require a generation of heat are logically irreversible ones, with the minimum heat generation being $kT \ln 2$ per bit of information lost. Nevertheless, it will be shown logical reversibility neither implies, nor is implied by thermodynamic reversibility. By examining thermodynamically reversible operations which are logically irreversible, it is possible to show that information and entropy, while having the same form, are conceptually different.