Effect of non-equilibrium term in two-particle correlation function on electron-phonon collision integrals

The derivation of kinetic equation for one-particle distribution function $F(p,r,t)$ from BBGKY chain leads to the collision integral expressed in terms of the two-particle correlation function. The latter is in turn expressed by $F$ using Boltzmann's Stosszahlansatz that implies the neglect of initial one-time correlation function $g2(p1,p2,r,t)$ which is non-diagonal in the momentum space. However, it has been established in non-equilibrium case that pair collisions generate the non-diagonal two-particle correlations that give the essential contribution to the current fluctuations of hot electrons. These correlations have been shown giving also a contribution to the collision integrals, i.e., to kinetic properties of nonequilibrium gas. The expression for electron energy loss rate $P$ via phonons is re-derived in detail from this point of view. The order of value of the new term in $P$ in the cases of acoustic- and optical-phonon scattering is evaluated in the electron temperature approximation using the experimental study of hot-electron energy relaxation time in $n-InSb$ at helium temperatures.