# Landauer's Principle for Trajectories of Repeated Interaction Systems

## TL;DR

This paper investigates Landauer's principle in quantum repeated interaction systems, establishing statistical properties of entropy production in the adiabatic limit, including large deviation principles and central limit theorems.

## Contribution

It provides a rigorous analysis of entropy production fluctuations in quantum systems under adiabatic conditions, extending previous results with a non-unitary adiabatic theorem and spectral analysis.

## Key findings

- Proved a large deviation principle for entropy production.
- Established a central limit theorem for the entropy production variable.
- Derived explicit limiting distributions in a special detailed balance case.

## Abstract

We analyze 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 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 deviation 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 obtain a non-unitary adiabatic theorem generalizing that of [Commun. Math. Phys. (2017) 349: 285] and analyze the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps.