What is the theoretical minimum power required for thrust relative to electric thrust

I understand that for a fixed massflow the minimum amount of power required to generate a thrust is: P = Massflow * ∫v dv = massflow *0.5* [v2^2 - v1^2]

However, is it possible to produce the same thrust with less power using the Lorentz force in an electromagnetic accelerator? If so, how can the above formula be the theoretical power requirement.

Any help is much appreciated. Cheers.