Abstract
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a certain symmetry in the Hamiltonian, which extends earlier work that has connected the large-deviation behavior of reversible stochastic processes to the gradient-flow structure of their deterministic limit. Natural examples of application include particle systems with inertia.
Original language | English |
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Pages (from-to) | 139-170 |
Number of pages | 32 |
Journal | Stochastic Processes and their Applications |
Volume | 130 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2020 |
Funding
R.K. was supported by the Deutsche Forschungsgemeinschaft (DFG), Germany via RTG 2131 High-dimensional Phenomena in Probability—Fluctuations and Discontinuity. A.L. was supported by the Interuniversity Attraction Pole - Phase VII/18 (Dynamics, Geometry and Statistical Physics) at the KU Leuven and the AFR PDR 2014–2 Grant No. 9202381 at the University of Luxembourg. M.A.P. was partially supported by NWO VICI grant 639.033.008 , The Netherlands.
Keywords
- Dynamical large deviations
- Fluctuation symmetry
- GENERIC
- Gradient flow