Landauer’s Principle for Trajectories of Repeated Interaction Systems

Abstract

We analyse Landauer’s principle for repeated interaction systems consisting of a reference quantum system $\mathcal {S}$ in contact with an environment $\mathcal {E}$ which is a chain of independent quantum probes. The system $\mathcal {S}$ interacts with each probe sequentially, for a given duration, and Landauer’s 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 with 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 deviation principle and a central limit theorem as $T \rightarrow \infty$ 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 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.