Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics
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| Format: | Preprint |
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2026
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| _version_ | 1866917363605045248 |
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| author | Bernardin, Cedric Gonçalves, Patricia Mangi, João Pedro |
| author_facet | Bernardin, Cedric Gonçalves, Patricia Mangi, João Pedro |
| contents | We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the corresponding stationary profile is characterized by a fractional Laplace equation. We establish a dynamical large deviations principle for the empirical measure and derive the associated stationary large deviations principle for the non-equilibrium steady state, which can be computed semi-explicitly. We further show that the stationary rate function coincides with the quasi-potential associated with the dynamical large deviations functional. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25957 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics Bernardin, Cedric Gonçalves, Patricia Mangi, João Pedro Probability We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the corresponding stationary profile is characterized by a fractional Laplace equation. We establish a dynamical large deviations principle for the empirical measure and derive the associated stationary large deviations principle for the non-equilibrium steady state, which can be computed semi-explicitly. We further show that the stationary rate function coincides with the quasi-potential associated with the dynamical large deviations functional. |
| title | Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics |
| topic | Probability |
| url | https://arxiv.org/abs/2603.25957 |