A set of "constrained probability densities" is constructed from the eigenstates of the transfer matrix for an Ising system and required to obey a set of reasonable regularity conditions. These densities yield constrained nonequilibrium generalizations of the entropy, internal energy, magnetization, and free energy. The behavior of these "constrained state functions", which are in general complex, is studied numerically for the Quasi-One-Dimensional Ising model, which approaches the mean-field limit as its interaction range N → ∞. Below the mean-field critical temperature the imaginary parts of the constrained entropy and free energy allow one to distinguish between stable, metastable, and unstable states, and they display finite-size scaling.