  In this paper, we study monotonicity formulas of eigenvalues and entropies
along the rescaled List's extended Ricci flow. We derive some monotonicity
formulas of eigenvalues of Laplacian which generalize those of Li in [8] and
Cao-Hou-Ling in [3]. Moreover, we also consider monotonicity formulas of
$\mathcal{F}_k$-functional which can be seen as a generalized
$\mathcal{F}$-functional corresponding with steady Ricci breathers, and
$\mathcal{W}_k$-functional which generalizes $\mathcal{W}$-functional
corresponding with expanding Ricci breathers.
