Violent relaxation in phase-space

The problem of violent relaxation mechanism in collisionless systems from the point of view of the distribution function (DF) in μ-space is reviewed. The literature run starts from the seminal paper of Lynden-Bell [Lynden-Bell, D., 1967. MNRAS 136, 101] and is closed by that of the same author [Arad, I., Lynden-Bell, D., 2005. MNRAS 361, 385]. After some introductive sections on the stellar dynamical equilibria and on the Shannon’s information theory, the different approaches follow each accompanied with its criticism on the previous works. Different coarse-grained DFs proposed by different authors have been taken into account. It appears that for a collisionless gas of a unique mass specie there is not significant discrepancies among the different approaches which converge to the same DF at the end of relaxation process. The main problem is to avoid the non observed mass segregation in the case of multi-species composition, e.g., in a star-dominated galaxy component. On this topic the results are very different and are depending on the shape and size one chooses for μ-space tiles. A great effort has been spent into the visualization of the different partitions in phase-space in order to understand clearly from what the differences arise.