  Calorimetry for equilibrium systems aims to determine the available
microscopic occupation and distribution of energy levels by measuring thermal
response. Nonequilibrium versions are expected to add information on the
dynamical accessibility of those states. We perform calculations on a driven
exclusion process on an array of particle stations, confirming that
expectation. That Markov model produces a fermionic nonequilibrium steady state
where the specific heat is computed exactly by evaluating the heat fluxes that
are entirely due to a change in ambient temperature. We observe a
zero-temperature divergence (violation of the Third Law) when the Fermi energy
and the kinetic barrier for loading and emptying become approximately equal.
Finally, when the kinetic barrier is density-dependent, a stable
low-temperature regime of negative specific heat appears, indicating an
anti-correlation between the temperature--dependence of the stationary
occupation and the excess heat.
