Charmonium production and suppression in heavy-ion collisions at relativistic energies is investigated within different models, i.e. the comover absorption model, the threshold suppression model, the statistical coalescence model and the HSD transport approach. In HSD the charmonium dissociation cross sections with mesons are described by a simple phase-space parametrization including an effective coupling strength |Mi| 2 for the charmonium states i = χc, J/ψ, ψ ′ . This allows to include the backward channels for charmonium reproduction by DD channels -which are missed in the comover absorption and threshold suppression model -employing detailed balance without introducing any new parameters. It is found that all approaches yield a reasonable description of J/ψ suppression in S+U and Pb+Pb collisions at SPS energies. However, they differ significantly in the ψ ′ /J/ψ ratio versus centrality at SPS and especially at RHIC energies. These pronounced differences can be exploited in future measurements at RHIC to distinguish the hadronic rescattering scenarios from quark coalescence close to the QGP phase boundary.

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Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulas for the microcanonical partition functions in the case of noninteracting massless neutral particles and charged particles with zero net charge. The particle number fluctuations are calculated and we find that in the microcanonical ensemble they are suppressed in comparison to the fluctuations in the canonical and grand canonical ensembles. This remains valid in the thermodynamic limit too, so that the well-known equivalence of all statistical ensembles refers to average quantities, but does not apply to fluctuations. In the thermodynamic limit we are able to calculate the particle number fluctuations in the system of massive bosons and fermions when the exact conservation laws of both the energy and charge are taken into account.