The Hall effect occurring in a Hall bar is revisited on the basis on non-equilibrium thermodynamics principles. Following the approach developed in a previous work (Creff et al. J. Appl. Phys 2020), the stationary state is defined by the minimum power dissipation principle, and the well-known results about the charge accumulation at the lateral edges and the corresponding Hall voltage are recovered. Beyond, the effect of a sizable current leakage occurring at the edges is investigated. An analytical expression of this output current - proportional to the magnetic field and the leakage resistance - is derived.