Ergodic properties of classical dissipative systems. I

DOI10.1007/BF02392587zbMath0976.37002OpenAlexW2032015191MaRDI QIDQ1282110

Claude-Alain Pillet, Vojkan Jakšić

Publication date: 6 January 2002

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392587

zbMATH Keywords

dissipative dynamical systemsergodicityLangevin equationOrnstein-Uhlenbeck processstochastic integro-differential equation

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31)

Related Items

Long-time asymptotics of solutions to a Hamiltonian system on a lattice, Hamiltonian and Lagrangian theory of viscoelasticity, Hamiltonian treatment of time dispersive and dissipative media within the linear response theory, On the asymptotical normality of statistical solutions for wave equations coupled to a particle, Plane wave stability analysis of Hartree and quantum dissipative systems, Recent progress on limit theorems for large stochastic particle systems, Nonequilibrium and fluctuation relation, On quantum dissipative systems: ground states and orbital stability, Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases, On convergence to equilibrium for one-dimensional chain of harmonic oscillators on the half-line, Control of fluctuations and heavy tails for heat variation in the two-time measurement framework, Hamiltonian structure for dispersive and dissipative dynamical systems, Discrete-time simulation of stochastic Volterra equations, Normal transport properties in a metastable stationary state for a classical particle coupled to a non-Ohmic bath, Ergodicity of stochastic differential equations driven by fractional Brownian motion, Exponential mixing under controllability conditions for \textsc{sde}s driven by a degenerate Poisson noise, Unnamed Item, Convergence to stationary states and energy current for infinite harmonic crystals

Cites Work

• The factorization of operator valued functions
• Ergodic properties of the non-Markovian Langevin equation
• On a model for quantum friction. II: Fermi's golden rule and dynamics at positive temperature
• On a model for quantum friction. III: Ergodic properties of the spin -- boson system
• Ergodic and quasideterministic properties of finite-dimensional stochastic systems
• Weighted trigonometrical approximation on \(R^ 1\) with application to the germ field of a stationary Gaussian noise
• On the factorization of matrices
• Statistical Mechanics of Assemblies of Coupled Oscillators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item