  The expression for the force on an ion in the presence of current can be
derived from first principles without any assumption about its conservative
character. However, energy functionals have been constructed that indicate that
this force can be written as the derivative of a potential function. On the
other hand, there exist compelling specific arguments that strongly suggest the
contrary. We propose physical mechanisms that invalidate such arguments and
demonstrate their existence with first-principles calculations. While our
results do not constitute a formal resolution to the fundamental question of
whether current-induced forces are conservative, they represent a substantial
step forward in this direction.
