  It is theoretically predicted that the Nernst coefficient is strongly
suppressed and the thermal conductance is quantized in the quantum Hall regime
of the two-dimensional electron gas. The Nernst effect is the induction of a
thermomagnetic electromotive force in the $y$ direction under a temperature
bias in the $x$ direction and a magnetic field in the $z$ direction. The
quantum nature of the Nernst effect is analyzed with the use of a circulating
edge current and is demonstrated numerically. The present system is a physical
realization of the non-equilibrium steady state.
