In this chapter, I explain how the evolution of an N-body system can be described using a formalism explicitly based on the distribution function in phase space. Such an approach can be contrasted with direct N-body simulations in which the trajectories of a large number of particles are integrated. Because trajectories with close initial conditions diverge exponentially in gravitational N-body systems (Goodman et al. 1993; Hemsendorf & Merritt 2002, and references therein), most results of N-body simulations must be interpreted statistically. It is therefore interesting to consider the simulation methods that treat the gravitational system in an explicitly statistical way.
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Freitag, M. (2008). Fokker–planck Treatment of Collisional Stellar Dynamics. In: Aarseth, S.J., Tout, C.A., Mardling, R.A. (eds) The Cambridge N-Body Lectures. Lecture Notes in Physics, vol 760. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8431-7_4
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