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.
Emergence of the Macroscopic Fourier Law from the Microscopic Wave Equation of Diffusive Medium
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abstract
The Fourier law and the diffusion equation are derived from the Schrodinger equation of a diffusive medium (consisting of a random potential). The theoretical model is backed by numerical simulation. This derivation can easily be generalized to demonstrate the transition from any random wave equation to the diffusive equation.
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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.