The transverse momentum spectra of different types of particles, ${\pi }^{\pm }$, $K^{\pm }$, p and $\overline{p}$, produced at mid-(pseudo)rapidity in different centrality lead–lead (Pb–Pb) collisions at 2.76 TeV; proton–lead (p–Pb) collisions at 5.02 TeV; xenon–xenon (Xe–Xe) collisions at 5.44 TeV; and proton–proton (p–p) collisions at 0.9, 2.76, 5.02, 7 and 13 TeV, were analyzed by the blast-wave model with fluctuations. With the experimental data measured by the ALICE and CMS Collaborations at the Large Hadron Collider (LHC), the kinetic freeze-out temperature, transverse flow velocity and proper time were extracted from fitting the transverse momentum spectra. In nucleus–nucleus (A–A) and proton–nucleus (p–A) collisions, the three parameters decrease with the decrease of event centrality from central to peripheral, indicating higher degrees of excitation, quicker expansion velocities and longer evolution times for central collisions. In p–p collisions, the kinetic freeze-out temperature is nearly invariant with the increase of energy, though the transverse flow velocity and proper time increase slightly, in the considered energy range.

Utilizing a partitioning method based on equal (or unequal) probabilities—without incorporating the alpha-cluster (α-cluster) model—allows for the derivation of diverse topological configurations of nuclear fragments resulting from fragmentation. Subsequently, we predict the multiplicity distribution of nuclear fragments for specific excited nuclei, such as ${}^9\mathrm{Be}^{*}$, ${}^{12}\mathrm{C}^{*}$, and ${}^{16}\mathrm{O}^{*}$, which can be formed as nuclear remnants in electron–nucleus ($eA$) collisions at high energy. Based on the $\alpha$-cluster model, an $\alpha$-cluster structure may result in deviations in the multiplicity distributions of nuclear fragments with charge $Z=2$, compared to those predicted by the partitioning methods. Furthermore, in the framework of Tsallis statistics, the nonextensive generalized temperature, entropy index, and q-entropy are obtained from the multiplicity distribution of nuclear fragments with a given charge number. Our work shows that fragmentation of nuclear remnants in electron–nucleus collisions at high energy is a nonextensive process.