  In this paper, we generalize the results of Laca, Larsen, and Neshveyev on
the $\mathrm{GL}_2$-Connes-Marcolli system to the $\mathrm{GL}_n$ systems. We
introduce the $\mathrm{GL}_n$-Connes-Marcolli systems and discuss the question
of the existence and the classification of KMS equilibrium states at different
inverse temperatures $\beta$. In particular, using an ergodicity argument, we
prove that in the range $n-1 <\beta\leq n$, there is only one KMS state. We
show that there are no KMS states for $\beta<n-1$ and not an integer, while we
construct KMS states for integer values of $\beta$ in the range $1\leq\beta\leq
n-1$, and we classify extremal KMS states for $\beta>n$.
