We study Landauer’s principle for repeated interaction systems consisting of a reference quantum system S in contact with an environment E made of a chain of independent quantum probes. The system S interacts with each probe sequentially, and the Landauer principle relates the energy variation of E and the decrease of entropy of S. We consider the adiabatic regime where the chain contains T probes and displays variations of order 1/T between the successive probes. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated with a two-time measurement protocol. At the technical level, our results rely on a non-unitary adiabatic theorem and and an analysis of the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps. This is joint work with Eric Hanson, Alain Joye and Renaud Raquépas.
Part of the Mathematics of Quantum Information workshop