Landauer's Principle in Repeated Interaction Systems

TL;DR

This paper investigates Landauer's Principle within repeated quantum interactions, establishing conditions for bound saturation and deriving a discrete adiabatic theorem to analyze energy-entropy relations in structured environments.

Contribution

It adapts Landauer's bound to discrete-time repeated interaction systems and introduces a non-unitary adiabatic theorem for analyzing the adiabatic limit.

Findings

Saturation of Landauer's bound corresponds to a detailed balance condition.

The study contrasts discrete repeated interactions with continuous open system dynamics.

A new adiabatic theorem for non-unitary quantum dynamics is established.

Abstract

We study Landauer's Principle for Repeated Interaction Systems (RIS) consisting of a reference quantum system $\mathcal{S}$ in contact with a structured environment $\mathcal{E}$ made of a chain of independent quantum probes; $\mathcal{S}$ interacts with each probe, for a fixed duration, in sequence. We first adapt Landauer's lower bound, which relates the energy variation of the environment $\mathcal{E}$ to a decrease of entropy of the system $\mathcal{S}$ during the evolution, to the peculiar discrete time dynamics of RIS. Then we consider RIS with a structured environment $\mathcal{E}$ displaying small variations of order $T^{-1}$ between the successive probes encountered by $\mathcal{S}$, after $n\simeq T$ interactions, in keeping with adiabatic scaling. We establish a discrete time non-unitary adiabatic theorem to approximate the reduced dynamics of $\mathcal{S}$ in this regime, in order to tackle the adiabatic limit of Landauer's bound. We find that saturation of Landauer's bound is equivalent to a detailed balance condition on the repeated interaction system, reflecting the non-equilibrium nature of the repeated interaction system dynamics. This is to be contrasted with the generic saturation of Landauer's bound known to hold for continuous time evolution of an open quantum system interacting with a single thermal reservoir in the adiabatic regime.