Deriving GENERIC from a Generalized Fluctuation Symmetry

2017/06/30 by Richard C. Kraaij, Richard Kraaij, Alexandre Lazarescu +3 · 32 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Geometry #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Statistical physics #Symmetry (geometry) #Theoretical and Computational Physics #Theoretical physics #cond-mat.stat-mech

paper · pdf · open access · doi:10.1007/s10955-017-1941-5

published in Journal of Statistical Physics 170(3), 492-508 (Springer Science+Business Media)

arxiv created 2017/06/30 · openalex publication_date 2017/12/14 · arxiv updated 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Much of the structure of macroscopic evolution equations for relaxation to equilibrium can be derived from symmetries in the dynamical fluctuations around the most typical trajectory. For example, detailed balance as expressed in terms of the Lagrangian for the path-space action leads to gradient zero-cost flow. We find a new such fluctuation symmetry that implies GENERIC, an extension of gradient flow where a Hamiltonian part is added to the dissipative term in such a way as to retain the free energy as Lyapunov function.

Citations

• The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
• Molecular dynamics simulations at constant pressure and/or temperature
• Dynamical density functional theory and its application to spinodal decomposition
• Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States
• Macroscopic fluctuation theory
• Time-Reversal and Entropy
• Dynamics and thermodynamics of complex fluids. I. Development of a general formalism
• Reciprocal Relations in Irreversible Processes. I.

Cited by

• Local detailed balance