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Lecture notes on large deviations in non-equilibrium diffusive systems
by Bernard Derrida
Submission summary
| Authors (as registered SciPost users): | Bernard Derrida |
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| Preprint Link: | scipost_202509_00019v1 (pdf) |
| Date accepted: | Sept. 16, 2025 |
| Date submitted: | Sept. 8, 2025, 4:54 p.m. |
| Submitted by: | Bernard Derrida |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
These notes are a written version of lectures given in the 2024 Les Houches Summer School on {\it Large deviations and applications}. They are are based on a series of works published over the last 25 years on steady properties of non-equilibrium systems in contact with several heat baths at different temperatures or several reservoirs of particles at different densities. After recalling some classical tools to study non-equilibrium steady states, such as the use of tilted matrices, the Fluctuation theorem, the determination of transport coefficients, the Einstein relations or fluctuating hydrodynamics, they describe some of the basic ideas of the macroscopic fluctuation theory allowing to determine the large deviation functions of the density and of the current of diffusive systems.
List of changes
Published as SciPost Phys. Lect. Notes 106 (2025)