Chemical and thermal equilibrium properties of infinite relativistic hadron matter are investigated using a microscopic transport model. This model is used to simulate the ultra-relativistic heavy ion collisions at different energy densities ε, namely the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). The molecular dynamics simulation is performed for a system of zero baryon number density and light meson species (π, ρ and K) in a box with periodic boundary conditions. The equilibrium state is investigated by studying the chemical equilibrium and the thermal equilibrium of the system. The particle multiplicity equilibrates with time, and the energy spectra of different light mesons species have the same slopes and common temperatures when thermal equilibrium is reached. This study shows the results of a full analysis of both chemical and thermal equilibrium before and after the system has reached the equilibrium state at different energy densities.