  We examine non-global and clustering logarithms in the distribution of the
azimuthal decorrelation between two jets in $e^+e^-\to$ dijet events, where the
jets are defined with $E$-scheme recombination in the generalized $k_t$
algorithm. We calculate at one loop and to all orders the leading global single
logarithms in the distribution of the said observable. We also compute at fixed
order up to four loops at finite $N_c$ the non-global and clustering
logarithms, and numerically resum them to all orders in the large-$N_c$
approximation. We compare our results at $\mathcal{O}(\alpha_s)$ and
$\mathcal{O}(\alpha_s^2)$ with those of the EVENT2 fixed-order Monte Carlo
program and find agreement of the leading singular behavior of the azimuthal
decorrelation distribution. We find that the impact of non-global logarithms on
the resummed distribution in the anti-$k_t$ algorithm is substantial, while it
is significantly smaller in the $k_t$ algorithm. Furthermore, the combined
clustering and non-global logarithms in the $k_t$ algorithm have an even
smaller effect on the distribution. Finally, we use the program Gnole to
calculate the resummed distribution at NLL accuracy, thus achieving
state-of-the-art accuracy for the resummation of this quantity.
