Savchuk O. The Equation of State of Strongly Interacting Matter and Relativistic Heavy-Ion Collisions

The theory of strong interactions, quantum chromodynamics, is well-defined mathematically. However, there is no reliable method for making predictions in the temperature range corresponding to the densities of ordinary nuclei and neutron stars, as well as parts of the early Universe. To explore the properties of such matter, like quarks and gluons, empirical knowledge obtained at accelerators of charged particles is required. Various observations made in experiments on heavy-ion collisions are described using different, usually phenomenological, models. The system that forms evolves, hence a dynamic description is important. Thus, standard approaches include relativistic hydrodynamics and transport models. Separately, the early or final stage may be described, making it important to build a self-consistent transition from one description to another. The properties of matter are regulated in a dynamic approach by specifying the interaction potential or the equation of state, which can be calculated using the methods of equilibrium statistical physics. Lattice quantum chromodynamics allows for obtaining knowledge about the properties of matter under conditions of zero baryonic charge. Extending lattice calculations to a finite baryonic potential is a theoretical challenge. It is important that any equation of state should coincide with lattice data. By calculating the Taylor series coefficients, which are related to the cumulants of charges, it is possible to analytically continue the lattice data to a finite baryonic potential. However, the convergence of the series may be limited by the singularity of the thermodynamic potential. The Lee-Yang theory relates singularities in the complex plane to phase transitions, and thus, by determining the radius of convergence of the series and the position of the singularity, it is possible to estimate the location of the critical point of deconfinement. However, there are also other, non-critical singularities, or other phase transitions that can also cause series divergence. As an example, a phase transition in nuclear matter, whose properties are considered well-studied, is considered. Since the coefficients of the pressure series expansion in terms of chemical potentials are related to fluctuations, it is considered that their measurement in relativistic heavy-ion collisions can become an important source of information about the equation of state. In practice, linking experiment to the equilibrium results of the statistical approach is a challenging task. Collisions are a dynamic process, and the density and temperature of the system change rather than correspond to a single point. Rapid changes in the properties of the medium can lead to memory effects associated with the finite relaxation time in the system. Moreover, detectors measure the final momenta of particles formed in relativistic collisions. Charge fluctuations that persist if all particles are observed should disappear. Therefore, a certain subsystem is usually considered. Classical statistical physics does not predict correlations between particle momenta. In this case, the probability of a particle entering the detection subspace or avoiding it should be described by a Bernoulli trial. The set of particles in this case corresponds to a binomial distribution. These assumptions are used to calculate the dependence of cumulants on the probability of detection and are compared with the predictions of the transport model. Deviations from the binomial distribution can indicate the existence of correlations in momentum space, which can be caused by conservation laws of energy and momentum, quantum effects, collective motion. The relationship between fluctuations in coordinate space and fluctuations in momentum space is considered in the method of subensembles. In this case, the statistical sum is divided into the product of statistical sums of subsystems, which are correlated exclusively by conservation laws, and any interactions between them are negligible (for example, the volume of each subsystem is much larger than the surface area between them). This allows calculating fluctuations as a function of the subsystem size under conditions of exact charge conservation and relating them to fluctuations in the grand canonical ensemble. In the presence of collective motion, different volumes may have different speeds of collective flows. Then, by selecting a certain speed or momentum, a certain volume of the system can be distinguished and compared with another momentum-volume. In this case, particle fluctuations should be strongly related to the equation of state.