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Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale

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Abstract

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.

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  1. Raphaël Chetrite

    Present address: Laboratoire J. A. Dieudonné, UMR CNRS 6621, Universitée de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice Cedex 02, France

  2. Shamik Gupta

    Present address: Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, 69364, Lyon cédex 07, France

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  1. Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel

    Raphaël Chetrite & Shamik Gupta

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  1. Raphaël Chetrite
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Chetrite, R., Gupta, S. Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale. J Stat Phys 143, 543–584 (2011). https://doi.org/10.1007/s10955-011-0184-0

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