  A dynamical method for inelastic transport simulations in nanostructures is
compared with a steady-state method based on non-equilibrium Green's functions.
A simplified form of the dynamical method produces, in the steady state in the
weak-coupling limit, effective self-energies analogous to those in the Born
Approximation due to electron-phonon coupling. The two methods are then
compared numerically on a resonant system consisting of a linear trimer weakly
embedded between metal electrodes. This system exhibits enhanced heating at
high biases and long phonon equilibration times. Despite the differences in
their formulation, the static and dynamical methods capture local
current-induced heating and inelastic corrections to the current with good
agreement over a wide range of conditions, except in the limit of very high
vibrational excitations, where differences begin to emerge.
