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

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.

References in corpus (11)

• Thermal Properties of Graphene, Carbon Nanotubes and Nanostructured Carbon Materials
• Thermal transport measurements of individual multiwalled nanotubes
• Thermal Conductance of an Individual Single-Wall Carbon Nanotube above Room Temperature
• Thermal Conductivity and Thermal Rectification in Graphene Nanoribbons: a Molecular Dynamics Study
• On the anomalous thermal conductivity of one-dimensional lattices
• Suppression of thermal conductivity in graphene nanoribbons with rough edges
• Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature
• A simple one-dimensional model of heat conduction which obeys Fourier's law
• Quantum thermal transport from classical molecular dynamics
• Molecular Dynamics Simulations of Heat Conduction in Nanostructures: Effect of Heat Bath
• The Derivation and Approximation of Coarse-grained Dynamics from Langevin Dynamics