Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

Marcus Kaiser, Robert Jack, Johannes Zimmer

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27 Citations (SciVal)


We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

Original languageEnglish
Pages (from-to)1019-1050
Number of pages32
JournalJournal of Statistical Physics
Issue number6
Early online date15 Feb 2018
Publication statusPublished - 1 Mar 2018


  • Irreversible Markov chains
  • Large deviations
  • Microscopic fluctuation theory
  • Nonequilibrium dynamical fluctuations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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