  In this paper, we continue development of the theory of contractive Markov
systems (CMS) initiated in \cite{Wer1}. Also, this work can be seen as a small
contribution to the theory of equilibrium states. We construct an energy
function on the code space, using the coding map from \cite{Wer3}, and show
that the generalized Markov measure associated with an irreducible CMS is a
unique equilibrium state for this energy function if the vertex sets form an
open partition of the state space of the CMS and the restrictions of the
probability functions on their vertex sets are Dini-continuous and bounded away
from zero.
