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The discreteness-driven relaxation of collisionless gravitating systems

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The violent relaxation of a perturbed or collapsing collisionless gravitational system, with the fast achievement of a quasi-stationary state, is traditionally assumed to be governed by the Vlasov equation, in which case the entropy must be conserved. In this scenario, the reconciliation with the 2nd law of thermodynamics is made through coarse-graining (a subjective effect). In this talk, I will discuss recent results obtained with entropy estimates in N-body simulations and for orbit ensembles in fixed external potentials. In the N-body simulations, the (slow) long-term evolution is well described as resulting from two-body relaxation, while the early evolution generates a fast (in a few crossing times) entropy production. The integration of orbit ensembles in external potentials shows that this early collisionless relaxation is due to the discreteness (finite N) of gravitating systems in any potential, being a consequence of the Nyquist-Shannon theorem, which precludes the development of phase-space structures finer than a typical scale N-1/d (for a sample of size N in d dimensions). As a result, a typical relaxation time T/tau_cr 0.1 * N1/6 emerges in integrable potentials, with weaker N-dependencies in the presence of chaotic orbits. Furthermore, this scenario avoids the need for the subjective effect of coarse-graining and indicates that the Vlasov equation does not provide an adequate kinetic description of this fast (violent) collisionless relaxation.

This talk is part of the Institute of Astronomy Galaxies Discussion Group series.

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