Chemical equilibration of U(1) charged particles in a thermal environment

We discuss chemical equilibration of particles carrying non-vanishing quantum numbers related with U(1) internal symmetry. We construct the transport equation for the time evolution of particle multiplicities and their probability functions. The solution of these equations is obtained in different limiting cases. It is argued that a U(1) charged particles, dependent on thermal conditions inside a fireball, approaches different equilibrium limits. The differences between kinetics of abundantly and rarely produced particles are explained.