Energy transfer dynamics and thermalization of two oscillators interacting via chaos.

We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment HE, 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 HE 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.