Hamiltonian model of heat conductivity and Fourier law

Abstract

We investigate the stationary nonequilibrium states of a quasi one-dimensional system of heavy particles whose interaction is mediated by purely elastic collisions with light particles, in contact at the boundary with two heat baths with fixed temperatures $T^{+}$ and $T^{-}$. It is shown that Fourier law is satisfied with a thermal conductivity proportional to $\sqrt{T(x)}$ where $T(x)$ is the local temperature. Entropy flux and entropy production are also investigated.

arXiv comment12 pages, 4 figures

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Cited by in corpus (5)

• Nonequilibrium Energy Profiles for a Class of 1-D Models
• Ising chain: Thermal conductivity and first-principle validation of Fourier law
• Analytic calculation of energy transfer and heat flux in a one-dimensional system
• Fourier's Law in a Generalized Piston Model
• First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model