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

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Abstract

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. 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 Macroscopic Fluctuation Theory, which describes hydrodynamic limits of such microscopic models.
Original languageEnglish
Pages (from-to)1019-1050
JournalJournal of Statistical Physics
Volume170
Issue number6
Early online date15 Feb 2018
DOIs
Publication statusPublished - 1 Mar 2018

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Fluctuations (theory)
Rate Function
Markov chains
orthogonality
Orthogonality
Markov chain
fluctuation theory
Fluctuation Theorem
Convergence to Equilibrium
Decompose
Hydrodynamic Limit
Continuous-time Markov Chain
Entropy Production
Large Deviations
decomposition
Dissipation
Term
dissipation
theorems
hydrodynamics

Cite this

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains. / Kaiser, Marcus; Jack, Robert; Zimmer, Johannes.

In: Journal of Statistical Physics, Vol. 170, No. 6, 01.03.2018, p. 1019-1050.

Research output: Contribution to journalArticle

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