Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics

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	Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics
	He, P
刊名	MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
	2012
卷号	419 期号:2 页码:1667-1681
关键词	NEGATIVE SPECIFIC HEAT DARK-MATTER HALOES VIOLENT RELAXATION STELLAR-SYSTEMS PHASE-SPACE SPHERICAL SYSTEMS ENTROPY PRINCIPLE H-FUNCTIONS STATES DENSITIES
ISSN号	0035-8711
通讯作者	He, P (reprint author), Jilin Univ, Coll Phys, Changchun 130021, Peoples R China.
英文摘要	The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless self-gravitating systems. We use an approach that is very different from that of the conventional statistical mechanics of short-range interaction systems. We demonstrate that the equilibrium states of self-gravitating systems consist of both mechanical and statistical equilibria, with the former characterized by a series of velocity-moment equations and the latter by statistical equilibrium equations, which should be derived from the entropy principle. The velocity-moment equations of all orders are derived from the steady-state collisionless Boltzmann equation. We point out that the ergodicity is invalid for the whole self-gravitating system, but it can be re-established locally. Based on the local ergodicity, using FermiDirac-like statistics, with the non-degenerate condition and the spatial independence of the local microstates, we rederive the BoltzmannGibbs entropy. This is consistent with the validity of the collisionless Boltzmann equation, and should be the correct entropy form for collisionless self-gravitating systems. Apart from the usual constraints of mass and energy conservation, we demonstrate that the series of moment or virialization equations must be included as additional constraints on the entropy functional when performing the variational calculus; this is an extension to the original prescription by White & Narayan. Any possible velocity distribution can be produced by the statistical-mechanical approach that we have developed with the extended BoltzmannGibbs/WhiteNarayan statistics. Finally, we discuss the questions of negative specific heat and ensemble inequivalence for self-gravitating systems.
学科主题	Physics
收录类别	SCI
资助信息	National Basic Research Programme of China [2010CB832805]
原文出处	http://dx.doi.org/10.1111/j.1365-2966.2011.19830.x
语种	英语
WOS记录号	WOS:000298482300066
公开日期	2014-04-25
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/15196]
专题	理论物理研究所_理论物理所1978-2010年知识产出
推荐引用方式 GB/T 7714	He, P. Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics[J]. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,2012,419(2):1667-1681.
APA	He, P.(2012).Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics.MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,419(2),1667-1681.
MLA	He, P."Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics".MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 419.2(2012):1667-1681.