Generalized Fourier's law in mesoscopic systems (opens in new tab)

Fourier's law fails when the mean free path of the energy carriers becomes comparable to the length and time scales over which the temperature field varies. We derive a thermodynamically consistent generalization in which the conductivity is promoted to a nonlocal memory operator $\bm{\kappa}_{\mathrm{eff}}(\mathbf{k},\omega)$, obtained by combining mesoscopic nonequilibrium thermodynamics with the Mori--Kubo--Zwanzig projection-operator formali...