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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 (MFT). For Markov chains, this theory involves a nonlinear 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 language  English 

Pages (fromto)  10191050 
Number of pages  32 
Journal  Journal of Statistical Physics 
Volume  170 
Issue number  6 
Early online date  15 Feb 2018 
DOIs  
Publication status  Published  1 Mar 2018 
Keywords
 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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 1 Finished

Analysis of the Effective Long TimeBehaviour of Molecule Systems
Zimmer, J.
Engineering and Physical Sciences Research Council
16/12/13 → 15/12/16
Project: Research council