Landauer's Principle for Trajectories of Repeated Interaction Systems

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.

48 pages, 4 figures; fixed typos, made cosmetic changes, and added Lemma 5.5. To appear in Annales Henri Poincaré

References in corpus (5)

• On entropy production of repeated quantum measurements I. General theory
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Landauer's Principle in Repeated Interaction Systems
• Random repeated interaction quantum systems
• A note on the Landauer principle in quantum statistical mechanics

Cited by in corpus (7)

• Nonequilibrium Dynamics with Finite-Time Repeated Interactions
• On entropy production of repeated quantum measurements II. Examples
• Eventually entanglement breaking Markovian dynamics: structure and characteristic times
• Markovian Repeated Interaction Quantum Systems
• Adiabatic Lindbladian Evolution with Small Dissipators
• Fermionic walkers driven out of equilibrium
• Quenched large deviations of Birkhoff sums along random quantum measurements