Irreversibility due to mixing in collisionless systems

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Galactic Structure, Irreversible Processes, Star Distribution, Chaos, Constraints, Distribution Functions, Galactic Evolution, Integral Equations, Mixing

Scientific paper

The stellar component of a galaxy can be described by the distribution function which gives the mass of stars per unit phase-space volume, with collisions being ignored. Such a system is believed to relax by a process of 'mixing' or coarse-graining. The mixing constraints derived by Tremaine et al. (1986) are reformulated for the case of a single distribution function, and it is shown how the distribution function together with other functions characterizing the configuration of a collisionless system can be used to obtain much stronger constraints on the final state of the system. The dynamical aspects of coarse-graining are discussed, and the question of whether equilibrium by mixing is attained is considered. The presence of chaotic effects on the evolution may require a redefinition of the concept of coarse-grained equilibrium.

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