[La loi de Fourier à la base de la dynamique microscopique]
Bien que la loi de Fourier soit confirmée empiriquement pour de nombreuses substances et sur un très large domaine de paramètres thermodynamiques, une dérivation microscopique convaincante pose encore des difficultés. Avec les machines actuelles, la solution des équations de mouvement de Newton peut être obtenues avec une grande précision et pour un nombre raisonnablement grand de particules. Pour les systèmes modèles simplifiés, on parvient ainsi à une compréhension plus approfondie de la base microscopique de la loi de Fourier. Nous discutons les progrès récents ainsi que ceux qui le sont moins.
While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines, the solution to Newton's equations of motion can be obtained with high precision and for a reasonably large number of particles. For simplified model systems, one thereby arrives at a deeper understanding of the microscopic basis for Fourier's law. We report on recent, and not so recent, advances.
Mot clés : Loi de Fourier, Simulation de la dynamique moléculaire, Formule de Green–Kubo
Abhishek Dhar 1 ; Herbert Spohn 2
@article{CRPHYS_2019__20_5_393_0,
author = {Abhishek Dhar and Herbert Spohn},
title = {Fourier's law based on microscopic dynamics},
journal = {Comptes Rendus. Physique},
pages = {393--401},
publisher = {Elsevier},
volume = {20},
number = {5},
year = {2019},
doi = {10.1016/j.crhy.2019.08.004},
language = {en},
}
Abhishek Dhar; Herbert Spohn. Fourier's law based on microscopic dynamics. Comptes Rendus. Physique, Volume 20 (2019) no. 5, pp. 393-401. doi : 10.1016/j.crhy.2019.08.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.08.004/
[1] Théorie Analytique de la Chaleur, Chez Firmin Didot, Paris, 1822 (Translated as: The Analytical Theory of Heat, 1878, Cambridge University Press, London)
[2] Fourier's law: a challenge to theorists (A. Fokas; A. Grigoryan; T. Kibble; B. Zegarlinski, eds.), Mathematical Physics 2000, Imperial College Press, London, 2000, p. 128
[3] Decay of the velocity autocorrelation function, Phys. Rev. A, Volume 1 (1970), p. 18
[4] Thermal conduction in classical low-dimensional lattices, Phys. Rep., Volume 377 (2003), p. 1
[5] Heat transport in low-dimensional systems, Adv. Phys., Volume 57 (2008), p. 457
[6] Non-equilibrium statistical mechanics of strongly anharmonic chains of oscillators, Commun. Math. Phys., Volume 212 (2000), p. 105
[7] Studies in molecular dynamics. VIII. The transport coefficients for a hard-sphere fluid, J. Chem. Phys., Volume 53 (1970), p. 3813
[8] One-dimensional classical many-body system having a normal thermal conductivity, Phys. Rev. Lett., Volume 52 (1984), p. 1861
[9] Heat conduction in chains of nonlinear oscillators, Phys. Rev. Lett., Volume 78 (1997), p. 1896
[10] Heat conduction in one-dimensional nonintegrable systems, Phys. Rev. E, Volume 61 (2000), p. 3828
[11] Non-equilibrium statistical mechanics of classical lattice field theory, Ann. Phys., Volume 295 (2002), p. 50
[12] Identifying diffusion processes in one-dimensional lattices in thermal equilibrium, Phys. Rev. Lett., Volume 96 (2006)
[13] Energy transport in weakly anharmonic chains, J. Stat. Phys., Volume 124 (2006), p. 1105
[14] Normal heat conductivity in a strongly pinned chain of anharmonic oscillators, J. Stat. Mech. Theory Exp., Volume L02001 (2006)
[15] Normal heat conductivity of the one-dimensional lattice with periodic potential of nearest-neighbor interaction, Phys. Rev. Lett., Volume 84 (2000), p. 2381
[16] Role of conserved quantities in normal heat transport in one dimension, 2015 | arXiv
[17] Coupled transport in rotor models, New J. Phys., Volume 18 (2016)
[18] Nonlinear fluctuating hydrodynamics for the classical XXZ spin chain, 2019 | arXiv
[19] Heat conduction in a three dimensional anharmonic crystal, Phys. Rev. Lett., Volume 104 (2010)
[20] Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer (S. Lepri, ed.), Lecture Notes in Physics, vol. 921, Springer International Publishing, 2016
[21] Anomalous energy transport in the FPU-β chain, Commun. Pure Appl. Math., Volume 61 (2008), p. 1753
[22] Dynamic correlators of Fermi-Pasta-Ulam chains and nonlinear fluctuating hydrodynamics, Phys. Rev. Lett., Volume 111 (2013)
[23] Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys., Volume 154 (2014), p. 1191
[24] Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain, Phys. Rev. E, Volume 90 (2014)
[25] Heat conduction in the Fermi–Pasta–Ulam chain, J. Stat. Phys., Volume 154 (2014), p. 204
[26] Normal heat conduction in one-dimensional momentum conserving lattices with asymmetric interactions, Phys. Rev. E, Volume 85 (2012) 060102(R)
[27] Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions, Phys. Rev. E, Volume 88 (2013)
[28] Heat conduction and phonon localization in disordered harmonic crystals, Europhys. Lett., Volume 90 (2010)
[29] Heat transport and phonon localization in mass-disordered harmonic crystals, Phys. Rev. B, Volume 81 (2010)
[30] Effect of phonon–phonon interactions on localization, Phys. Rev. Lett., Volume 100 (2008)
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