Time-Reversibility, Instability and Thermodynamics in N-body Systems Interacting with Long-Range Potentials

Long-range attractive potentials cause self-gravitating N-body systems to exhibit not only chaotic behavior but also peculiar features such as gravothermal catastrophe, negative specific heat and nonextensive statistical mechanics. Especially when its potential energy is significantly dominated, a system should gradually evolve from quasi-equilibrium states through collapses to core-halo states. In dynamical evolution, velocity distributions are generally expected to monotonically relax from non-Gaussian towards Gaussian (Maxwell–Boltzmann) distributions. To clarify the velocity relaxation, we numerically examine the long-term evolution of a self-gravitating N-body system enclosed in a spherical container with adiabatic walls. We found that the velocity distribution non-monotonically relaxes from a non-Gaussian distribution to a Gaussian-like distribution when a core forms rapidly through the collapse process.