Heat-current relaxation time (${\tau }_Q$)

A heat-current relaxation time measures the decay of a departure from equilibrium carrying heat. It need not equal the momentum relaxation time or the time between arbitrary scattering events. In an isotropic degenerate-electron estimate, $K_e=c_e{v}_F^2{\tau }_Q/3$. Small-angle inelastic electron-phonon scattering can remove an excitation energy of order $k_{B}T$ while barely changing the electron's velocity direction, thus relaxing heat more efficiently than charge flow.