  A measurement of novel event shapes quantifying the isotropy of collider
events is performed in 140 fb$^{-1}$ of proton-proton collisions with $\sqrt
s=13$ TeV centre-of-mass energy recorded with the ATLAS detector at CERN's
Large Hadron Collider. These event shapes are defined as the Wasserstein
distance between collider events and isotropic reference geometries. This
distance is evaluated by solving optimal transport problems, using the
'Energy-Mover's Distance'. Isotropic references with cylindrical and circular
symmetries are studied, to probe the symmetries of interest at hadron
colliders. The novel event-shape observables defined in this way are infrared-
and collinear-safe, have improved dynamic range and have greater sensitivity to
isotropic radiation patterns than other event shapes. The measured event-shape
variables are corrected for detector effects, and presented in inclusive bins
of jet multiplicity and the scalar sum of the two leading jets' transverse
momenta. The measured distributions are provided as inputs to future Monte
Carlo tuning campaigns and other studies probing fundamental properties of QCD
and the production of hadronic final states up to the TeV-scale.
