Spatially-resolved voltage-reversal due to Bernoulli potentials in dissipative Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$

We measure magneto-transport and critical currents in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ Hall bar devices. Above critical current in an applied magnetic field, we observe longitudinal differential voltage along one edge comparable in magnitude but opposite in sign to the other edge. This phenomenon is unaffected by reversal of the applied field, and seems unique to devices with invasive voltage contacts. We attribute the source of this behavior to particle-hole symmetry breaking in moving vortices and the formation of opposite Bernoulli potentials due to opposing vortex velocities at the edges where the invasive contacts create hotspots for rapid vortex nucleation and flux flow. These results are fundamental to the composition and flow of dissipative currents in layered superconductors.