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The ALICE Collaboration reports the first fully-corrected measurements of the$N$-subjettiness observable for track-based jets in heavy-ion collisions. Thisstudy is performed using data recorded in pp and Pb$-$Pb collisions atcentre-of-mass energies of $\sqrt{s} = 7$ TeV and $\sqrt{s_{\rm NN}} =2.76$\,TeV, respectively. In particular the ratio of 2-subjettiness to1-subjettiness, $\tau_{2}/\tau_{1}$, which is sensitive to the rate oftwo-pronged jet substructure, is presented. Energy loss of jets traversing thestrongly interacting medium in heavy-ion collisions is expected to change therate of two-pronged substructure relative to vacuum. The results are presentedfor jets with a resolution parameter of $R = 0.4$ and charged jet transversemomentum of $40 \leq p_{\rm T,\rm jet} \leq 60$ GeV/$c$, which constitute alarger jet resolution and lower jet transverse momentum interval than previousmeasurements in heavy-ion collisions. This has been achieved by utilising asemi-inclusive hadron-jet coincidence technique to suppress the larger jetcombinatorial background in this kinematic region. No significant modificationof the $\tau_{2}/\tau_{1}$ observable for track-based jets in Pb--Pb collisionsis observed relative to vacuum PYTHIA6 and PYTHIA8 references at the samecollision energy. The measurements of $\tau_{2}/\tau_{1}$, together with thesplitting aperture angle $\Delta R$, are also performed in pp collisions at$\sqrt{s}=7$ TeV for inclusive jets. These results are compared with PYTHIAcalculations at $\sqrt{s}=7$ TeV, in order to validate the model as a vacuumreference for the Pb$-$Pb centre-of-mass energy. The PYTHIA references for$\tau_{2}/\tau_{1}$ are shifted to larger values compared to the measurement inpp collisions. This hints at a reduction in the rate of two-pronged jets inPb--Pb collisions compared to pp collisions.

First measurements of $N$-subjettiness in central Pb$-$Pb collisions at ${\sqrt{\it{s}_{\rm {NN}}}} = 2.76$ TeV