A variational extension of the Keldysh formalism to spatially varying temperature yields a heat equation and a proposed Tolman thermal equivalence principle linking non-equilibrium flat-space fermions to equilibrium curved-space fermions.
Fourier's Law from Closure Equations
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We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.
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Phonon Gravity, Non-equilibrium QFT, and the Tolman Thermal Equivalence Principle
A variational extension of the Keldysh formalism to spatially varying temperature yields a heat equation and a proposed Tolman thermal equivalence principle linking non-equilibrium flat-space fermions to equilibrium curved-space fermions.