Landauer's Principle for Trajectories of Repeated Interaction Systems

A refinement and generalization of our previous work on Landauer’s Principle in repeated interaction systems. We consider a two-time measurement protocol of the energy of the quantum probes, and recover a large deviations principle and a central limit theorem in the adiabatic limit of a repeated interaction system. Abstract: “We analyze Landauer’s principle for repeated interaction systems consisting of a reference quantum system \(\mathcal{S}\) in contact with a environment \(\mathcal{E}\) consisting of a chain of independent quantum probes. The system \(\mathcal{S}\) interacts with each probe sequentially, for a given duration, and the Landauer principle relates the energy variation of \(\mathcal{E}\) and the decrease of entropy of \(\mathcal{S}\) by the entropy production of the dynamical process. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated to a two-time measurement protocol of, essentially, the energy of \(\mathcal{E}\) . The emphasis is put on the adiabatic regime where the environment, consisting of \(T\gg 1\) probes, displays variations of order \(T^{-1}\) between the successive probes, and the measurements take place initially and after \(T\) interactions. We prove a large deviations principle and a central limit theorem as \(T\to\infty\) for the classical random variable describing the entropy production of the process, with respect to the FS measure. In a special case, related to a detailed balance condition, we obtain an explicit limiting distribution of this random variable without rescaling. At the technical level, we generalize the discrete non-unitary adiabatic theorem by the present authors in [Commun. Math. Phys. (2017) 349: 285] and analyze the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps."