Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems

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Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exists. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, n ( E ) ∝ exp ( − β ( E − Φ 0 ) ) − 1 , known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark matter halos with central cusps, ρ ∼ r −1, and outer parts, ρ ∼ r −4. Here we define a nonequilibrium functional, S D , which is maximized for DARKexp and increases monotonically during the evolution toward equilibrium of idealized collisionless systems of the extended spherical infall model. Systems that undergo more mixing more closely approach DARKexp.

Original languageEnglish (US)
Article number67
JournalAstrophysical Journal
Issue number2
StatePublished - Oct 1 2022
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank the anonymous referee for their insightful comments. We thank Scott Tremaine for challenging us to demonstrate the existence of an entropy-like functional that evolves monotonically with time and reaches DARKexp as the maximum entropy state. We are grateful to Jeppe Dyre, Rafael Fernandez, Alex Kamenev, Yongzhong Qian, Panagiotis Tolias, Jenny Wagner, and Radek Wojtak for insightful comments. J.H. was supported by a VILLUM FONDEN Investigator grant (project No. 16599).

Publisher Copyright:
© 2022. The Author(s). Published by the American Astronomical Society.


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