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Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

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Abstract

We consider an irreducible continuous-time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for the empirical measure and current. By contraction, we get the large deviation principle of three types of entropy production flow. We derive some Gallavotti–Cohen duality relations and discuss some applications.

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Acknowledgements

We thank the anonymous referees for their careful reading and suggestions. A. Faggionato and D. Gabrielli thank the Institute Henri Poincaré for the kind hospitality and the support during the trimester “Stochastic Dynamics Out of Equilibrium,” in which they have worked on the manuscript.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le Aldo Moro 2, 00185, Rome, Italy

    Lorenzo Bertini & Alessandra Faggionato

  2. CNRS Laboratoire J.A. Dieudonné, Université Côte d’Azur, 06108, Nice Cedex 2, France

    Raphael Chetrite

  3. Department of Physics Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan

    Raphael Chetrite

  4. DISIM Università dell’Aquila, Via Vetoio, Loc. Coppito, 67100, L’Aquila, Italy

    Davide Gabrielli

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  1. Lorenzo Bertini
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  2. Raphael Chetrite
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  3. Alessandra Faggionato
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  4. Davide Gabrielli
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Correspondence to Alessandra Faggionato.

Additional information

Communicated by Christian Maes.

The work of L. Bertini and A. Faggionato has been supported by PRIN 20155PAWZB “Large Scale Random Structures,” while the work of R. Chetrite has been supported by the French Ministry of Education Grant ANR-15-CE40-0020-01.

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Bertini, L., Chetrite, R., Faggionato, A. et al. Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates. Ann. Henri Poincaré 19, 3197–3238 (2018). https://doi.org/10.1007/s00023-018-0705-3

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