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题名: Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics
作者: He, P
刊名: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
出版日期: 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
学科分类: Physics
通讯作者: He, P (reprint author), Jilin Univ, Coll Phys, Changchun 130021, Peoples R China.
部门归属: [He, Ping] Jilin Univ, Coll Phys, Changchun 130021, Peoples R China; [He, Ping] Chinese Acad Sci, Key Lab Frontiers Theoret Phys, Inst Theoret Phys, Beijing 100190, 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.
资助者: National Basic Research Programme of China [2010CB832805]
收录类别: SCI
原文出处: 查看原文
语种: 英语
WOS记录号: WOS:000298482300066
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/15196
Appears in Collections:理论物理所2012年知识产出_期刊论文

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Recommended Citation:
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.
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