On Landauer's principle and bound for infinite systems

Understand

Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy.

• We set up here a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view.
• By the Tomita-Takesaki modular theory, we can indeed describe a canonical evolution associated with a quantum channel state transfer.
• Such evolution is implemented both by a modular Hamiltonian and a physical Hamiltonian, the latter being determined by its functoriality properties.