Peltier effect induced longitudinal resistivity of ideal 2D   electron(hole) gas in strong magnetic field
  We demonstrate that in strong quantum limit the thermoelectric Peltier effect could define the longitudinal resistivity of dissipationless two-dimensional electron(hole) gas. The current results in heating(cooling) at first(second) Hall bar sample contact due to Peltier effect. At small current the contacts temperatures are different, the temperature gradient is linear on current. The voltage swing downstream the current is proportional to Peltier effect induced thermopower. As a result, nonzero longitudinal resistivity is measured in experiment. The above effect could exist in 3D case. 
M.V.Cheremisin