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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2501.00679 |
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| _version_ | 1866912572365602816 |
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| author | Crawford, David E. Zeng, Yi Vidal, Judith Dong, Jianjun |
| author_facet | Crawford, David E. Zeng, Yi Vidal, Judith Dong, Jianjun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theory of Transient Heat Conduction Crawford, David E. Zeng, Yi Vidal, Judith Dong, Jianjun Materials Science Mesoscale and Nanoscale Physics Computational Physics 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. |
| title | Theory of Transient Heat Conduction |
| topic | Materials Science Mesoscale and Nanoscale Physics Computational Physics |
| url | https://arxiv.org/abs/2501.00679 |