Our analysis of reacting systems displaced from equilibrium by a matter flux across the boundaries has shown that the state of minimum entropy production differs from the steady state, even in the near equilibrium regime. When the displacement 6 from equilibrium is small, the derivative of the dissipation at the steady state and the dissipation itself are both of order 8'. The state of least dissipation is displaced from the steady state by terms of order 8' in the species concentrations. The theorem of minimum entropy production may be derived by first truncating the series expansions for the reaction rates, affinities and dissipation assuming that 6 is small, and then differentiating to locate the minimum of the dissipation within the resulting idealized model. For chemical systems with an arbitrarily small but macroscopic displacement from equilibrium, this truncation procedure establishes that the dissipation is comparatively small in a neighborhood of the steady state; but it causes large relative errors in the values of the concentration derivatives and time derivatives of the dissipation within that neighborhood, because the operations of series truncation and differentiation do not commute near the steady state, when S is small but nonzero. Near the steady state, the concentration derivative of the term of order 6' in the dissipation is comparable to or larger than the derivative of the 6' term.