Theory of Transient Heat Conduction

TL;DR

This paper develops a unified, microscopic theory of transient heat conduction that connects atomic-scale mechanisms with macroscopic transport, enabling better understanding and simulation of ultrafast, nanoscale heat transfer phenomena.

Contribution

It introduces a time-domain transport function based on statistical physics, bridging microscopic heat flux correlations with macroscopic conduction behavior.

Findings

Generalizes Fourier's law for transient regimes

Describes transition from wave-like to diffusive heat conduction

Applicable to bulk materials at all temperatures and scales

Abstract

Ultrafast and nanoscale heat conduction demands a unified theoretical framework that rigorously bridges macroscopic transport equations with microscopic material properties derived from statistical physics.Existing empirical generalizations of Fourier's law often lack a solid microscopic foundation, failing to connect observed non-Fourier behavior with underlying atomic scale mechanisms. In this work, we present a time-domain theory of transient heat conduction rooted in Zwanzig's statistical theory of irreversible processes. Central to this framework is the time-domain transport function, Z(t), defined through equilibrium time-correlation functions of heat fluxes. This function generalizes the conventional concept of steady-state thermal conductivity, governing the transition of conduction dynamics from onset second sound type wave propagation at finite speeds to diffusion-dominated behavior across broad temporal and spatial scales. Unlike phonon hydrodynamic models that rely on mesoscopic constructs such as phonon drift velocity, our approach provides a quantitative and microscopic description of intrinsic memory effects in transient heat fluxes and applies universally to bulk materials at any temperature or length scale. By integrating atomistic-scale first-principles calculations with continuum-level macroscopic equations, this framework offers a robust foundation for numerical simulations of transient temperature fields. Furthermore, it facilitates the interpretation and design of transient thermal grating experiments using nanometer-scale heat sources and ultrafast laser systems in the extreme ultraviolet and x-ray wavelength ranges, advancing our understanding of heat dissipation dynamics.