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Linear Response Theory and Entropic Fluctuations in Repeated Interaction Quantum Systems

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Abstract

We study linear response theory and entropic fluctuations of finite dimensional non-equilibrium Repeated Interaction Systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green–Kubo fluctuation–dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation Principle, or Fluctuation Theorem, and a Central Limit Theorem on the full counting statistics of entropy fluxes. We consider two types of non-equilibrium RIS: either the temperatures of the probes are deterministic and arrive in a cyclic way, or the temperatures of the probes are described by a sequence of i.i.d. random variables with uniform distribution over a finite set.

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Acknowledgements

This research was supported by the Agence Nationale de la Recherche through the grant NONSTOPS (ANR-17-CE40-0006) and by the Initiative d’excellence Paris-Seine. The research of JFB is partially funded by the Cross Disciplinary Program “Quantum Engineering Grenoble”. LB warmly thanks UMI-CRM of Montreal for financial support and McGill University for its hospitality during an earlier stage of this work. We thank the anonymous referees for their constructive remarks and suggestions.

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  1. Département de Mathématiques and UMR 8088, CNRS and CY Cergy Paris Université, 95000, Cergy-Pontoise, France

    Jean-François Bougron & Laurent Bruneau

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

    Jean-François Bougron

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  1. Jean-François Bougron
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  2. Laurent Bruneau
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Correspondence to Laurent Bruneau.

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Communicated by Yoshiko Ogata.

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Bougron, JF., Bruneau, L. Linear Response Theory and Entropic Fluctuations in Repeated Interaction Quantum Systems. J Stat Phys 181, 1636–1677 (2020). https://doi.org/10.1007/s10955-020-02640-x

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