A Mechanical Model for Fourier’s Law of Heat Conduction

被引：0
|
作者：
David Ruelle
机构：
[1] Rutgers University,Mathematics Department
[2] Hill Center,undefined
[3] IHES,undefined
来源：
Communications in Mathematical Physics | 2012年 / 311卷
关键词：
Microscopic Dynamic; Nonequilibrium Statistical Mechanic; Local Unstable Manifold; Smooth Dynamic; Major Unsolved Problem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Nonequilibrium statistical mechanics close to equilibrium is a physically satisfactory theory centered on the linear response formula of Green-Kubo. This formula results from a formal first order perturbation calculation without rigorous justification. A rigorous derivation of Fourier’s law for heat conduction from the laws of mechanics remains thus a major unsolved problem. In this note we present a deterministic mechanical model of a heat-conducting chain with nontrivial interactions, where kinetic energy fluctuations at the nodes of the chain are removed. In this model the derivation of Fourier’s law can proceed rigorously.
引用
收藏
页码：755 / 768
页数：13
相关论文
共 50 条
  • [31] Beyond the Fourier heat conduction law and the thermal no-slip boundary condition
    Lebon, G.
    Jou, D.
    Dauby, P. C.
    PHYSICS LETTERS A, 2012, 376 (45) : 2842 - 2846
  • [32] Exponential and polynomial decay for a laminated beam with Fourier's law of heat conduction and possible absence of structural damping
    Liu, Wenjun
    Zhao, Weifan
    FRONTIERS OF MATHEMATICS IN CHINA, 2021, 16 (04) : 997 - 1021
  • [33] Fourier’s heat conduction equation: History, influence, and connections
    T. N. Narasimhan
    Proceedings of the Indian Academy of Sciences - Earth and Planetary Sciences, 1999, 108 (3): : 117 - 148
  • [34] Fourier's heat conduction equation: History, influence, and connections
    Narasimhan, TN
    REVIEWS OF GEOPHYSICS, 1999, 37 (01) : 151 - 172
  • [35] Exponential and polynomial decay for a laminated beam with Fourier’s law of heat conduction and possible absence of structural damping
    Wenjun Liu
    Weifan Zhao
    Frontiers of Mathematics in China, 2021, 16 : 997 - 1021
  • [36] The Ohm-Fourier law of conduction
    不详
    ZEITSCHRIFT FUR ELEKTROCHEMIE UND ANGEWANDTE PHYSIKALISCHE CHEMIE, 1928, 34 : 753 - 756
  • [37] Generalization of Fourier's Law into Viscous Heat Equations
    Simoncelli, Michele
    Marzari, Nicola
    Cepellotti, Andrea
    PHYSICAL REVIEW X, 2020, 10 (01)
  • [38] Measuring heat flux beyond Fourier's law
    Smith, E. R.
    Daivis, P. J.
    Todd, B. D.
    JOURNAL OF CHEMICAL PHYSICS, 2019, 150 (06):
  • [39] Microscopic quantum mechanical foundation of Fourier's law
    Michel, Mathias
    Gemmer, Jochen
    Mahler, Guenter
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2006, 20 (29): : 4855 - 4883
  • [40] Second Law Considerations in Fourier Heat Conduction of a Lattice Chain in Relation to Intermolecular Potentials
    Jesudason, Christopher G.
    ICNPAA 2016 WORLD CONGRESS: 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES, 2017, 1798
12345