Bagchi, D.,Tsallis, C.

The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (beta type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t > t(eq), the temperature arid energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time t(eq) depends on the system size N as t(eq) similar to N-gamma where gamma similar or equal to 1.8. We compute the velocity distribution P(v) of the oscillators of the two systems during the relaxation process. We find that P(v) is non Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t = t(eq) the value of q converges to unity and P(v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.