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Landauer’s Principle in Repeated Interaction Systems

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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 related 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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, 805 rue Sherbrooke Ouest, Montréal, QC, H3A 0B9, Canada

    Eric P. Hanson & Renaud Raquépas

  2. Université Grenoble Alpes CNRS, Institut Fourier, 38000, Grenoble, France

    Alain Joye

  3. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405, Orsay, France

    Yan Pautrat

Authors
  1. Eric P. Hanson
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  2. Alain Joye
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  3. Yan Pautrat
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  4. Renaud Raquépas
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Correspondence to Yan Pautrat.

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Communicated by R. Seiringer

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Hanson, E.P., Joye, A., Pautrat, Y. et al. Landauer’s Principle in Repeated Interaction Systems. Commun. Math. Phys. 349, 285–327 (2017). https://doi.org/10.1007/s00220-016-2751-3

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