The system of Escherichia coli infected by λ phage is one of the templates for quantitative study of regulated networks. In this article, according to the characteristics of the interactions between operators and regulators, the probabilities of regulators binding to operators are described by thermodynamic partition function. On the basis of bifurcation analysis of this regulated network, the entropies of stationary states are calculated. Results show that the entropies of both lysogenic state and lytic state are lower than those of saddle-point and bifurcation point states. Moreover, we find that the lysogenic state has lower entropy than lytic state, which proves that the lysogenic state has a higher biological order.