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

  • Raphaël Chetrite
  • Shamik Gupta
Article

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.

Keywords

Non-equilibrium Markov Process Fluctuation-Dissipation Theorems Fluctuation Relations Martingales 

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Authors and Affiliations

  1. 1.Physics of Complex SystemsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Laboratoire J. A. Dieudonné, UMR CNRS 6621Universitée de Nice Sophia-AntipolisNice Cedex 02France
  3. 3.Laboratoire de Physique de l’École Normale Supérieure de LyonUniversité de Lyon, CNRSLyon cédex 07France

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