Abstract: We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment H-E, consisting of N noninteracting chaotic systems. The parameters are set so that when either particle is separately placed in contact with the environment, a dissipative behavior is observed. When both particles are simultaneously in contact with H-E an indirect coupling between them is observed only if the particles are in near-resonance. We study the equilibrium properties of the system considering ensemble averages for the case N = 1 and single trajectory dynamics for N large. In both cases, the particles and the environment reach an equilibrium configuration at long times, but only for large N can a temperature be assigned to the system Ver menos