  Measurements of differential top quark pair $\mathrm{t\overline{t}}$ cross
sections using events produced in proton-proton collisions at a centre-of-mass
energy of 13 TeV containing two oppositely charged leptons are presented. The
data were recorded by the CMS experiment at the CERN LHC in 2016 and correspond
to an integrated luminosity of 35.9 fb$^{-1}$. The differential cross sections
are presented as functions of kinematic observables of the top quarks and their
decay products, the $\mathrm{t\overline{t}}$ system, and the total number of
jets in the event. The differential cross sections are defined both with
particle-level objects in a fiducial phase space close to that of the detector
acceptance and with parton-level top quarks in the full phase space. All
results are compared with standard model predictions from Monte Carlo
simulations with next-to-leading-order (NLO) accuracy in quantum chromodynamics
(QCD) at matrix-element level interfaced to parton-shower simulations. Where
possible, parton-level results are compared to calculations with beyond-NLO
precision in QCD. Significant disagreement is observed between data and all
predictions for several observables. The measurements are used to constrain the
top quark chromomagnetic dipole moment in an effective field theory framework
at NLO in QCD and to extract $\mathrm{t\overline{t}}$ and leptonic charge
asymmetries.
