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Macroscopic Fluctuation Theory versus large-deviation-induced GENERIC

D. R. Michiel Renger

Abstract

Recent developments in Macroscopic Fluctuation Theory show that many interacting particle systems behave macroscopically as a combination of a gradient flow with Hamiltonian dynamics. This observation leads to the natural question how these structures compare to the GENERIC framework. This paper serves as a brief survey of both fields and a comparison between them, including a number of example models to which the comparison results are applied.

Macroscopic Fluctuation Theory versus large-deviation-induced GENERIC

Abstract

Recent developments in Macroscopic Fluctuation Theory show that many interacting particle systems behave macroscopically as a combination of a gradient flow with Hamiltonian dynamics. This observation leads to the natural question how these structures compare to the GENERIC framework. This paper serves as a brief survey of both fields and a comparison between them, including a number of example models to which the comparison results are applied.
Paper Structure (58 sections, 25 theorems, 147 equations, 1 table)

This paper contains 58 sections, 25 theorems, 147 equations, 1 table.

Table of Contents

  1. Introduction
  2. Level of description
  3. Force vs. flux splitting
  4. Outline
  5. Mathematical framework
  6. Survey on MFT
  7. Micro to macro properties
  8. Force structure and decomposition
  9. Fisher information and ergodic limit (new insight)
  10. Symmetric flow
  11. Antisymmetric flow
  12. Further decomposition by generalised orthogonality
  13. An interpretation of generalised orthogonality (new insight)
  14. Applications of the decomposition
  15. MANERIC definitions
  16. ...and 43 more sections

Key Result

Proposition 2.3

Let the following LDPs hold: Then:

Theorems & Definitions (62)

  • Definition 2.1
  • Remark 2.2
  • Proposition 2.3: BDSGJLL2015MFT,Renger2018a,PattersonRengerSharma2024
  • Definition 2.4
  • Proposition 2.5: BDSGJLL2015MFT,MielkePeletierRenger2014,Renger2018a,RengerZimmer2021,PattersonRengerSharma2024
  • Remark 2.6
  • Remark 2.7
  • Remark 2.8
  • Remark 2.9
  • Theorem 2.10
  • ...and 52 more