The ALICE experiment is one of the major detectors at the CERN Large Hadron Collider, specifically designed to study strongly interacting matter at extreme energy densities. Its primary goal is to investigate the properties of the quark–gluon plasma (QGP), a state of matter believed to have existed microseconds after the Big Bang. ALICE focuses on heavy-ion collisions, such as lead–lead (Pb–Pb) interactions, where thousands of particles are produced. Its sophisticated tracking and particle identification systems allow precise measurements of hadrons, leptons, and photons over a wide momentum range. This makes it uniquely suited to study collective behavior, particle production, and QCD phenomena in hot and dense nuclear matter. Through these studies, ALICE provides key insights into deconfinement, chiral symmetry restoration, and the transport properties of the QGP, contributing significantly to our understanding of quantum chromodynamics under extreme conditions.

Event-shape observables characterize the geometrical structure of particle production in high-energy collisions, providing insight into the underlying dynamics beyond simple multiplicity measurements. Quantities such as spherocity and flattenicity are used to distinguish between jet-like (anisotropic) and isotropic events. Flattenicity, in particular, is designed to quantify how uniformly particles are distributed in the transverse plane. It is typically constructed from the distribution of particle densities across azimuthal segments of the detector. Low flattenicity values correspond to events with strong azimuthal anisotropy (jet-dominated), while high values indicate a more uniform, isotropic particle distribution, often associated with soft, multi-particle production. Such observables are especially useful in experiments like the ALICE experiment, where they help classify events and study the interplay between hard and soft QCD processes, as well as possible collective effects in small systems like proton–proton collisions.

Heavy-flavor and quarkonium measurements provide some of the most sensitive probes of the hot and dense medium created in high-energy nuclear collisions. Heavy quarks (charm and beauty), produced predominantly in the early stages of the collision, experience the full space–time evolution of the medium and thus carry information about its transport properties. Observables such as nuclear modification factors and elliptic flow reveal how these quarks lose energy and participate in the collective motion of the system. Quarkonia states (e.g., charmonium and bottomonium) are particularly valuable because their binding is affected by color screening in the deconfined medium. The suppression and possible regeneration of these states provide complementary information about the temperature and density of the quark–gluon plasma. Charm diffusion, quantified through the spatial diffusion coefficient (D_s), characterizes how charm quarks propagate through the medium. Its magnitude is directly related to the coupling strength between heavy quarks and the surrounding plasma: a small (D_s) indicates strong interactions and near-thermalization, while a larger value points to weaker coupling. Precise measurements, particularly from experiments like the ALICE experiment, help constrain theoretical models and improve our understanding of transport phenomena in quantum chromodynamics.

The hadron resonance gas (HRG) model describes strongly interacting matter in the confined phase as a non-interacting gas of all known hadrons and resonances. It successfully reproduces particle yields in heavy-ion collisions and provides a useful baseline for thermodynamic quantities near the QCD crossover, consistent with results from lattice QCD at low temperatures. Under extreme conditions, such as high temperature, finite baryon density, strong magnetic fields, or rotation, the HRG framework can be extended to include medium effects. These include modifications of particle dispersion relations, inclusion of magnetic-field-dependent Landau quantization, and rotational contributions to thermodynamics. Such extensions allow the study of magnetization, spin polarization, and equation-of-state changes in environments relevant to heavy-ion collisions and compact astrophysical objects. These generalized HRG approaches serve as a bridge between hadronic and partonic descriptions, helping to isolate signals of deconfinement and understand how hadronic matter responds to external fields and vorticity.

Non-extensive statistics, based on the Tsallis statistics framework, extends conventional Boltzmann–Gibbs thermodynamics to systems that may exhibit long-range correlations, intrinsic fluctuations, or non-equilibrium effects. In high-energy collisions, Tsallis distributions have been widely used to successfully describe transverse momentum spectra over a broad range, effectively capturing both soft (thermal) and hard (power-law) components within a single formalism. In the context of the hadron resonance gas (HRG), incorporating non-extensive effects modifies the equilibrium distribution functions, leading to changes in thermodynamic quantities such as pressure, energy density, and particle yields. These modifications can mimic interactions or deviations from equilibrium, offering an alternative way to interpret freeze-out conditions and particle production in heavy-ion and even small-system collisions. For transport properties in HRG and QCD matter, non-extensive statistics can influence quantities like shear and bulk viscosities, diffusion coefficients, and relaxation times. The non-extensive parameter (q) effectively encodes the degree of deviation from equilibrium, with (q \to 1) recovering the standard results. This approach provides a phenomenological bridge between microscopic dynamics and macroscopic observables, helping to explore how fluctuations and correlations impact the behavior of strongly interacting matter.

High-temperature Bose–Einstein condensation in the context of strongly interacting matter refers to the possibility that bosonic degrees of freedom (e.g., pions or gluonic modes) undergo macroscopic occupation of the ground state even in environments with relatively large temperatures, provided other conditions, such as high density or modified dispersion relations are satisfied. In heavy-ion physics, pion condensation has been discussed in scenarios with large isospin chemical potential, where the effective mass of pions decreases and can approach zero, triggering condensation despite the thermal background. Similarly, in QCD-inspired models, gluon overpopulation in the early stages of the collision has been argued to potentially lead to a transient Bose–Einstein condensate before full thermalization. The key point is that “high temperature” does not preclude condensation if the phase-space density is sufficiently large. Thus, studies of Bose–Einstein condensation under extreme conditions provide insight into non-equilibrium dynamics, overoccupied systems, and possible novel phases of QCD matter beyond the conventional quark–gluon plasma picture.