The reversible version of the smallest chemical reaction system with Hopf bifurcation is analyzed. This simple scheme, which contains only mono- and bimolecular reactions, can serve as a model for demonstrating different kinetic and thermodynamic analytical techniques. It is shown that a subcritical Hopf bifurcation, which is excluded in the system with irreversible reactions, as well as a saddle-node bifurcation of the limit cycle occur in the reversible case. Furthermore, implications for the dynamic behavior are discussed when the system is embedded in a larger reaction network. Different techniques of the thermodynamic stability analysis of equilibrium and nonequilibrium steady states are compared with the usual kinetic analysis. The excess entropy which is the basis for the local analysis is also used as a Lyapunov function for a global stability analysis and compared to Shear's function.