  We obtain the quark and gluon rapidity anomalous dimension to fourth order in
QCD. We calculate the N$^3$LO rapidity anomalous dimensions to higher order in
the dimensional regulator and make use of the soft/rapidity anomalous dimension
correspondence in conjunction with the recent determination of the N$^4$LO
threshold anomalous dimensions to achieve our result. We show that the results
for the quark and gluon rapidity anomalous dimensions at four loops are related
by generalized Casimir scaling. Using the N$^4$LO rapidity anomalous dimension,
we perform the resummation of the Energy-Energy Correlation in the back-to-back
limit at N$^4$LL, achieving for the first time the resummation of an event
shape at this logarithmic order. We present numerical results and observe a
reduction of perturbative uncertainties on the resummed cross section to below
1%.
