Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective

DOI10.1007/s10955-024-03233-8arXiv2103.14384OpenAlexW3147935684MaRDI QIDQ6189807

Robert I. A. Patterson, D. R. Michiel Renger, Upanshu Sharma

Publication date: 5 February 2024

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.14384

Mathematics Subject Classification ID

Markov processes (60Jxx) Time-dependent statistical mechanics (dynamic and nonequilibrium) (82Cxx) Limit theorems in probability theory (60Fxx)

Cites Work

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• Formulation of thermoelastic dissipative material behavior using GENERIC
• Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion
• On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
• Product-form stationary distributions for deficiency zero chemical reaction networks
• From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage
• Lyapunov functions, stationary distributions, and non-equilibrium potential for reaction networks
• Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
• Implicit time discretization for the mean curvature flow equation
• Macroscopic fluctuation theory for stationary nonequilibrium states
• Canonical structure and orthogonality of forces and currents in irreversible Markov chains
• Large deviations for mixtures
• A technique for exponential change of measure for Markov processes
• Flux large deviations of independent and reacting particle systems, with implications for macroscopic fluctuation theory
• Orthogonality of fluxes in general nonlinear reaction networks
• Flux large deviations of weakly interacting jump processes via well-posedness of an associated Hamilton-Jacobi equation
• Large deviations for Markov jump processes with uniformly diminishing rates
• Is the Boltzmann equation reversible? A large deviation perspective on the irreversibility paradox
• Large deviations of jump process fluxes
• Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation
• An inequality connecting entropy distance, Fisher information and large deviations
• Variational approach to coarse-graining of generalized gradient flows
• Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations
• Dynamical phase transitions for flows on finite graphs
• Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
• On geometry of multiscale mass action law and its fluctuations
• GENERIC formalism of a Vlasov–Fokker–Planck equation and connection to large-deviation principles
• Large deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conduction
• Convex Optimization in Normed Spaces
• Large Deviations of the Empirical Current in Interacting Particle Systems
• On A Class Of Doubly Nonlinear Evolution Equations
• Markov Chains
• Random perturbations of Hamiltonian systems
• Reciprocal Relations in Irreversible Processes. II.
• Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• Detailed balance, local detailed balance, and global potential for stochastic chemical reaction networks
• Asymptotics of the Invariant Measure in Mean Field Models with Jumps
• Non-equilibrium Thermodynamical Principles for Chemical Reactions with Mass-Action Kinetics
• Non-Dissipative Effects in Nonequilibrium Systems
• A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
• Large deviations and gradient flows
• Solutions of ordinary differential equations as limits of pure jump markov processes
• Fluctuations and Irreversible Processes
• Non-reversible processes: GENERIC, hypocoercivity and fluctuations
• Fast reaction limits via \(\Gamma\)-convergence of the flux rate functional
• Large deviations of Kac's conservative particle system and energy nonconserving solutions to the Boltzmann equation: a counterexample to the predicted rate function

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