Landauer’s Principle for Trajectories of Repeated Interaction Systems

We analyse Landauer’s principle for repeated interaction systems consisting of a reference quantum system S in contact with an environment E which is a chain of independent quantum probes. The system S interacts with each probe sequentially, for a given duration, and Landauer’s principle relates the energy variation of E and the decrease of entropy of 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 with a two-time measurement protocol of, essentially, the energy of E. The emphasis is put on the adiabatic regime where the environment, consisting of T≫ 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 deviation principle and a central limit theorem as T→ ∞ 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 obtain a non-unitary adiabatic theorem generalizing that of Hanson et al. (Commun Math Phys 349(1):285–327, 2017) and analyse the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps.

Duke Scholars

Author Renaud Raquépas Mathematics