2019/09/01 by Alyx Jourjine, Jourjine, Alyx
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Electrodynamics and Casimir Effect #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.1909.00396
openalex publication_date 2019/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe an extension of the Keldysh method for fermions from constant\ntemperature to steady state case with spatially varying temperature field.This\nis done with the use on the imaginary section of the Keldysh path of a thermal\nHamiltonian obtained from the zero temperature relativistic Hamiltonian by\ncoupling its density multiplicatively to the temperature field. We show that\nthe two Hamiltonians commute, provided appropriate boundary conditions are\nimposed. A microscopical equation on the temperature field and the\ncorresponding microscopical Fourier law of heat transfer are derived for the\nrelativistic and the non-relativistic cases. We discuss application of the\nproposed method to the thermoelectric effect and point out a remarkable\ncorrespondence between the non-equilibrium thermal Hamiltonian and the zero\ntemperature fermionic Hamiltonian in general relativity for the metric obtained\nfrom the Minkowski metric by rescaling time with the inverse temperature.Our\nresults suggest the existence of the correspondence principle between\ngravitating equilibrium and non-gravitating non-equilibrium quantum field\ntheories, which we call the Tolman thermal equivalence principle in honor of\nhis pioneering work.\n