### 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 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 language | English |
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Pages (from-to) | 1019-1050 |

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*170*(6), 1019-1050. https://doi.org/10.1007/s10955-018-1986-0

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 170, no. 6, pp. 1019-1050. https://doi.org/10.1007/s10955-018-1986-0

}

TY - JOUR

T1 - Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

AU - Kaiser, Marcus

AU - Jack, Robert

AU - Zimmer, Johannes

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - Irreversible Markov chains

KW - Large deviations

KW - Microscopic fluctuation theory

KW - Nonequilibrium dynamical fluctuations

UR - http://www.scopus.com/inward/record.url?scp=85042110297&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-1986-0

DO - 10.1007/s10955-018-1986-0

M3 - Article

VL - 170

SP - 1019

EP - 1050

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -