Unified Statistical Theory of Heat Conduction in Nonuniform Media

[2507.05682] Unified Statistical Theory of Heat Conduction in Nonuniform Media Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Materials Science arXiv:2507.05682 (cond-mat) [Submitted on 8 Jul 2025 ( v1 ), last revised 14 Apr 2026 (this version, v2)] Title: Unified Statistical Theory of Heat Conduction in Nonuniform Media Authors: Yi Zeng , Jianjun Dong View a PDF of the paper titled Unified Statistical Theory of Heat Conduction in Nonuniform Media, by Yi Zeng and Jianjun Dong View PDF HTML (experimental) Abstract: Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal memory, spatial nonlocality, and material heterogeneity on equal footing. Classical diffusion, nonlocal transport, and hydrodynamic models emerge as controlled asymptotic limits of this kernel, providing a unified constitutive description across diffusive, quasi-ballistic, and hydrodynamic regimes. Interfacial heat transfer is incorporated through a spatially resolved kernel formulation, in which the conventional Kapitza resistance arises as a coarse-grained limit. The kernel admits a spatiotemporal Green--Kubo representation and can, in principle, be evaluated from atomistic simulations for bulk media, providing a direct connection between microscopic dynamics and continuum transport without empirical closure. For crystalline solids, we derive explicit kernel forms in the hydrodynamic and attenuated-streaming limits and introduce a hybrid reduction that captures the coexistence of collective and quasi-ballistic transport. For disordered harmonic solids, the framework recovers a spatial diffusion kernel consistent with the Allen--Feldman limit. To illustrate the theory, we construct the kernel for silicon at room temperature within the relaxation-time approximation and apply it to transient thermal grating configurations. Spatial nonlocality associated with the phonon mean-free-path distribution is the primary source of deviation from Fourier transport under these conditions, while temporal memory mainly influences short-time dynamics. These findings identify the spatiotemporal kernel as a unifying constitutive descriptor whose coarse-grained limits recover conventional transport coefficients. Comments: 35 pages, 6 figures and 2 tables Subjects: Materials Science (cond-mat.mtrl-sci) ; Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2507.05682 [cond-mat.mtrl-sci] (or arXiv:2507.05682v2 [cond-mat.mtrl-sci] for this version) https://doi.org/10.48550/arXiv.2507.05682 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yi Zeng [ view email ] [v1] Tue, 8 Jul 2025 05:21:09 UTC (36 KB) [v2] Tue, 14 Apr 2026 06:04:17 UTC (2,006 KB) Full-text links: Access Paper: View a PDF of the paper titled Unified Statistical Theory of Heat Conduction in Nonuniform Media, by Yi Zeng and Jianjun Dong View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.mtrl-sci < prev | next > new | recent | 2025-07 Change to browse by: cond-mat cond-mat.mes-hall References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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