Hoppenau, Johannes and Nickelsen, Daniel and Engel, Andreas
(2016)
*Level 2 and level 2.5 large deviation functionals for systems with and without detailed balance.*
New journal of physics , 18 (083010).
pp. 1-18.
ISSN 1367-2630

## Abstract

Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 or level 2.5 large deviation functional characterizing the empirical density and current of the underlying stochastic process. For Langevin systems obeying detailed balance, the explicit form of the level 2 functional has been known ever since the mathematical work of Donsker and Varadhan. We rederive the Donskerâ€“Varadhan result using stochastic path-integrals. We than generalize the derivation to level 2.5 large deviation functionals for non-equilibrium steady states and elucidate the relation between the large deviation functionals and different notions of entropy production in stochastic thermodynamics. Finally, we discuss some aspects of the contractions to level 1 large deviation functions and illustrate our findings with examples.

Item Type: | Article |
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Subjects: | Science and mathematics > Science Science and mathematics > Mathematics Science and mathematics > Physics |

Divisions: | Faculty of Mathematics and Science > Institute of Physics (IfP) |

Date Deposited: | 07 Feb 2017 13:12 |

Last Modified: | 07 Feb 2017 13:12 |

URI: | https://oops.uni-oldenburg.de/id/eprint/2957 |

URN: | urn:nbn:de:gbv:715-oops-30387 |

DOI: | 10.1088/1367-2630/18/8/083010 |

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