ANALYTICAL MECHANICS IN STOCHASTIC DYNAMICS: MOST PROBABLE PATH, LARGE-DEVIATION RATE FUNCTION AND HAMILTON–JACOBI EQUATION

DOI10.1142/S0217979212300125zbMath1274.82043arXiv1205.6052MaRDI QIDQ2861303

Hong Qian, Hao Ge

Publication date: 12 November 2013

Published in: International Journal of Modern Physics B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.6052

zbMATH Keywords

Hamilton-Jacobi equationstochastic dynamicslarge deviationsFreidlin-Wentzell theorylandscapeexponentially small asymptoticsmost probable pathexcess kinetic energy

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to statistical mechanics (82-02) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

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A machine learning method for computing quasi-potential of stochastic dynamical systems ⋮ A decomposition of irreversible diffusion processes without detailed balance ⋮ One‐Dimensional Birth‐Death Process and Delbrück‐Gillespie Theory of Mesoscopic Nonlinear Chemical Reactions ⋮ The zeroth law of thermodynamics and volume-preserving conservative system in equilibrium with stochastic damping ⋮ First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions ⋮ The statistical foundation of entropy in extended irreversible thermodynamics

Cites Work

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• Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
• Mapping between dissipative and Hamiltonian systems
• Existence and construction of dynamical potential in nonequilibrium processes without detailed balance
• Fluctuations and Irreversible Processes

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