GENERIC formalism of a Vlasov–Fokker–Planck equation and connection to large-deviation principles

From MaRDI portal
Publication:2864560

DOI10.1088/0951-7715/26/11/2951zbMath1288.60029arXiv1302.1024OpenAlexW3105523643WikidataQ59873988 ScholiaQ59873988MaRDI QIDQ2864560

Manh Hong Duong, Johannes Zimmer, Mark Adriaan Peletier

Publication date: 25 November 2013

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.1024




Related Items (39)

Formulation of the relativistic heat equation and the relativistic kinetic Fokker-Planck equations using GENERICGENERIC framework for the Fokker-Planck equationA gradient flow approach to large deviations for diffusion processesLarge deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conductionOn the fundamental solution and a variational formulation for a degenerate diffusion of Kolmogorov typeA minimizing-movements approach to GENERIC systemsVariational approach to coarse-graining of generalized gradient flowsAn entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic modelsQuantification of coarse-graining error in Langevin and overdamped Langevin dynamicsGradient structures for the thermomechanics of shape-memory materialsAccurate and robust splitting methods for the generalized Langevin equation with a positive prony series memory kernelA new minimizing-movements scheme for curves of maximal slopeEntropic Regularization of NonGradient SystemsOperator-splitting schemes for degenerate, non-local, conservative-dissipative systemsFrom continuum mechanics to SPH particle systems and back: Systematic derivation and convergenceEnergetically consistent model reduction for metriplectic systemsExploring families of energy-dissipation landscapes via tilting: three types of EDP convergenceA symplectic Brezis-Ekeland-Nayroles principle for dynamic plasticity in finite strainsLarge deviations and gradient flows for the Brownian one-dimensional hard-rod systemGENERIC framework for reactive fluid flowsA variational principle of minimum for Navier-Stokes equation based on the symplectic formalismStationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transitionThe regularised inertial Dean–Kawasaki equation: discontinuous Galerkin approximation and modelling for low-density regimeVariational structures beyond gradient flows: a macroscopic fluctuation-theory perspectiveBarriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measuresOn the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusionA Regularized Dean--Kawasaki Model: Derivation and AnalysisLong time behaviour and particle approximation of a generalised Vlasov dynamicQuadratic and rate-independent limits for a large-deviations functionalDeriving GENERIC from a generalized fluctuation symmetryCoupling Rate-Independent and Rate-Dependent Processes: Existence ResultsFluctuation symmetry leads to GENERIC equations with non-quadratic dissipationFrom weakly interacting particles to a regularised Dean–Kawasaki modelJump processes as generalized gradient flowsThe fourth law of thermodynamics: steepest entropy ascentTwo structure-preserving time discretizations for gradient flowsThe Markov process admits a consistent steady-state thermodynamic formalismStochastic gradient descent and fast relaxation to thermodynamic equilibrium: A stochastic control approachNon-reversible processes: GENERIC, hypocoercivity and fluctuations


Uses Software



This page was built for publication: GENERIC formalism of a Vlasov–Fokker–Planck equation and connection to large-deviation principles