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This paper presents a kinetic theory model of gravitational collapse due to asmall perturbation. Solving the relevant equations yields a pattern of entropydestruction in a spherical core around the perturbation, and entropy creationin a surrounding halo. This indicates collisional "de-relaxation" in the core,and collisional relaxation in the halo. Core-halo patterns are ubiquitous inthe astrophysics of gravitational collapse, and are found here without any ofthe prior assumptions of such a pattern usually made in analytical models.Motivated by this analysis, the paper outlines a possible scheme foridentifying structure formation in a set of observations or a simulation. Thisscheme involves a choice of coarse-graining scale appropriate to the structureunder consideration, and might aid exploration of hierarchical structureformation, supplementing the usual density-based methods for highlightingastrophysical and cosmological structure at various scales.

A core-halo pattern of entropy creation in gravitational collapse