Landauer's Principle in Repeated Interaction Systems

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.

Linked entropy production to detailed balance relation, improved presentation, and added concluding section

References in corpus (4)

• Quantum Operation Time Reversal
• General Adiabatic Evolution with a Gap Condition
• Random repeated interaction quantum systems
• A note on the Landauer principle in quantum statistical mechanics

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• Linear response theory and entropic fluctuations in repeated interaction quantum systems
• Markovian Repeated Interaction Quantum Systems
• Adiabatic theorems for general linear operators with time-independent domains
• Adiabatic Lindbladian Evolution with Small Dissipators
• Thermal state preparation by repeated interactions at and beyond the Lindblad limit
• Fermionic walkers driven out of equilibrium
• Interpolated Collision Model Formalism
• Entropy Production of Quantum Reset Models
• Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle