The Mori-Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics

2017/08/03 by Weiqi Chu, Xiantao Li, Chu, Weiqi +1
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Thermal properties of materials

paper · pdf · doi:10.48550/arxiv.1709.05928

openalex publication_date 2017/08/03 · openalex created_date 2017/09/25 · openalex updated_date 2026/07/28

Abstract

Energy transport equations are derived directly from full molecular dynamics models as coarse-grained description. With the local energy chosen as the coarse-grained variables, we apply the Mori-Zwanzig formalism to derive a reduced model, in the form of a generalized Langevin equation. A Markovian embedding technique is then introduced to eliminate the history dependence. In sharp contrast to conventional energy transport models, this derivation yields \it stochastic dynamics models for the spatially averaged energy. We discuss the approximation of the random force using both additive and multiplicative noises, to ensure the correct statistics of the solution.

Citations

• The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models
• Perspective: Coarse-grained models for biomolecular systems
• A molecular dynamics method for simulations in the canonical ensemble

Related

• Energy fluctuations in simple conduction models
• Coarse-grained Mori-Zwanzig dynamics in a time-non-local stationary-action framework
• Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism
• Fixing the flux: A dual approach to computing transport coefficients
• Hamiltonian Brownian motion in Gaussian thermally fluctuating potential. I. Exact Langevin equations, invalidity of Marcovian approximation, common bottleneck of dynamic noise theories, and diffusivity/mobility 1/f noise