Langevin equation for hot-electron problems

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Abstract
In this paper, we build a Langevin equation for the macrovariables of an electronic system in contact with a lattice, when the entire system is in the hot-electron regime. A bridge is established between this equation and earlier ones which give the thermodynamic motion of these microvariables. Finally, by focusing on the Langevin equation for the electronic momentum of the system, we examine the causes of the failure of the first fluctuation-dissipation theorem in its usual form in the stationary (far-from-equilibrium) situation.