A reduction scheme for coupled Brownian harmonic oscillators
arXiv:2209.13481 · doi:10.1088/1751-8121/acab41
Abstract
We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original dynamics and is written in terms of suitable transport coefficients. The proposed procedure is twofold: while the deterministic component of the dynamics is obtained by a direct application of the invariant manifold method, the diffusion terms are determined via the Fluctuation-Dissipation Theorem. We highlight the behavior of the coefficients up to a critical value of the coupling parameter, which marks the endpoint of the interval in which a contracted description is available. The study of the weak coupling regime is addressed and the commutativity of alternative reduction paths is also discussed.
References in corpus (23)
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
- Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
- Effective dynamics using conditional expectations
- Hilbert's 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations
- Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph
- Exact dynamical coarse-graining without time-scale separation
- Model reduction for networks of coupled oscillators
- Reduced-Order Models for Coupled Dynamical Systems: Data-driven Methods and the Koopman Operator
- Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics
- Kinetic models for polymers with inertial effects
- Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part I: Theory
- Exact linear hydrodynamics from the Boltzmann equation
- Boltzmann equation and hydrodynamic fluctuations
- From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations
- Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad's equations
- Nonequilibrium Statistical Mechanics and Optimal Prediction of Partially-Observed Complex Systems
- Model Reduction for the Kuramoto-Sakaguchi Model: The Importance of Non-entrained Rogue Oscillators
- Effective dynamics for non-reversible stochastic differential equations: a quantitative study
- Effect of Inertia on Linear Viscoelasticity of Harmonic Dumbbell Model
- Edgeworth expansions for slow-fast systems with finite time scale separation
- Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory
- Quantitative coarse-graining of Markov chains