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.
On Unsteady Heat Conduction in a Harmonic Crystal
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abstract
An analytical model of unsteady heat transfer in a one-dimensional harmonic crystal is presented. A nonlocal temperature is introduced as a generalization of the kinetic temperature. A closed equation determining unsteady thermal processes in terms of the nonlocal temperature is derived. For an instantaneous heat perturbation a time-reversible equation for the kinetic temperature is derived and solved. The resulting constitutive law for the heat flux in the considered system is obtained. This law significantly differs from Fourier's law and it predicts a finite velocity of the heat front and independence of the heat flux on the crystal length. The analytical results are confirmed by computer simulations.
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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.