http://arxiv.org/abs/1706.03487
Making a simple model of gravitational collapse in cosmology and astrophysics, this paper examines the creation and destruction of kinetic theory entropy after a small perturbation is introduced into a homogeneous distribution of self-gravitating particles. To keep the problem tractable, gravity is Newtonian and the focus is on a coarse-grained slice of entropy constructed from the one- and two-particle distribution functions. The slice chosen is asymptotically-dominant, in the sense that it will eventually dominate over all other entropy associated with a given scale within the system. Its entropy is destroyed within a central sphere near the initial location of the perturbation – the core – and created in a surrounding shell – the halo. The core-halo transition radii are not fixed, but are proportional to the coarse-graining length used. At leading order, creation and destruction are in balance. At next-to-leading order, destruction predominates, the rate of destruction being proportional to an exponent of the time elapsed after the perturbation was introduced, and further proportional to the square of the perturbation size, divided by the square of the coarse-graining volume. For late times, destruction of asymptotic coarse-grained entropy is at least offset by entropy creation ever further from the central perturbation. We can interpret this as gravitational collapse leading to local large-scale structure formation – that is, destruction of coarse-grained entropy – at least offset by ever more distant creation of disorder. Making a plausible assumption about the application of the second law of thermodynamics to coarse-grained entropy, that distant disorder would itself be large scale.
A. Wren
Tue, 13 Jun 17
60/92
Comments: 47 pages, 10 figures. Mathematica notebooks available from Github at this https URL . Comments welcome
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