  To be useful, steady state thermodynamics (SST) must be self-consistent and
have predictive value. Although consistency of SST was recently verified for
driven lattice gases under global weak exchange, I show here that it does not
predict the coexisting densities in athermal stochastic lattice gases under a
nonuniform drive. I consider the lattice gas with nearest-neighbor exclusion on
the square lattice, with nearest-neighbor hopping (NNE dynamics), and with
hopping to both nearest and next-nearest neighbors (NNE2 dynamics). Part of the
system is subject to a drive $D$ that favors hopping along one direction, while
the other part is free of the drive. Thus the steady state represents
coexistence between two subsystems, one far from equilibrium and the other in
equilibrium, which exchange particles along the interfaces. The dimensionless
chemical potential $\mu^*(\rho,D) = \mu/k_B T$ for the lattice gas with density
$\rho$ is readily determined in studies of a uniform system. Under the
nonuniform drive, however, equating the chemical potentials of the coexisting
subsystems does not yield the coexisting densities. The steady state chemical
potential is, moreover, different in the coexisting bulk regions, contrary to
the basic principles of thermodynamics. These results cast serious doubt on the
predictive value of SST.
