Nonlinear Constitutive Models for Nano-scale Heat Conduction

TL;DR

This paper develops a rigorous, statistically consistent nonlinear stochastic model for transient heat conduction at the nanoscale, derived from a many-particle all-atom description.

Contribution

It introduces a novel approach that derives nonlinear stochastic constitutive relations for nanoscale heat conduction from first principles.

Findings

Derivation of a nonlinear stochastic constitutive model

Ensures statistical consistency with all-atom descriptions

Provides a framework for modeling nanoscale heat transfer

Abstract

We present a rigorous approach that leads, from a many-particle description, to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at nanoscale. By enforcing statistical consistency, in that the statistics of the local energy is consistent with that from an all-atom description, we identify the driving force as well as the model parameters in these generalized constitutive models.