  We show that the non-equilibrium steady state (NESS) of the free lattice
Fermion model far from equilibrium is macroscopically unstable. The problem is
translated to that of the spectral analysis of {\it Liouville Operator}. We use
the method of positive commutators to investigate it. We construct a positive
commutator on the lattice Fermion system, whose dispersion relation is
$\omega(k)=\cos k-\gamma$.
