We present a detailed study of the entropy production, the entropy exchange and the entropy balance for the Schlögl model of chemical bi-stability for both the clamped and volumetric open-flow versions. The general evolution criterion (GEC) is validated for the transitions from the unstable to the stable non-equilibrium stationary states. The GEC is the sole theorem governing the temporal behavior of the entropy production in non-equilibrium thermodynamics, and we find no evidence for supporting a "principle" of maximum entropy production. We use stoichiometric network analysis (SNA) to calculate the distribution of the entropy production and the exchange entropy over the elementary flux modes of the clamped and open-flow models, and aim to reveal the underlying mechanisms of dissipation and entropy exchange.