Quantum Hall Effect: the resistivity of a two-dimensional electron gas using a thermodynamic approach

Based on a thermodynamic approach, we have calculated the resistivity of a 2D electron gas, assumed $dissipationless$ in a strong quantum limit. Standard measurements, with extra current leads, define the resistivity caused by a combination of Peltier and Seebeck effects. The current causes heating(cooling) at the first(second) sample contacts, due to the Peltier effect. The contact temperatures are different. The measured voltage is equal to the Peltier effect-induced thermoemf which is linear in current. As a result, the resistivity is non-zero as $I\to 0$. The resistivity is a universal function of magnetic field and temperature, expressed in fundamental units $h/e^{2}$. The universal features of magnetotransport data observed in experiment confirm our predictions.