Entropy principle and complementary second law of thermodynamics for self-gravitating systems

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	Entropy principle and complementary second law of thermodynamics for self-gravitating systems
	He, Ping; Kang, Dong-Biao; He, P , Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China
刊名	MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
	2010
卷号	406 期号:4 页码:2678-2688
关键词	Dark-matter Halos Universal Density Profile Violent Relaxation Statistical-mechanics Phase-space Velocity Anisotropy Stellar-systems Galaxy Clusters H-functions Evolution
ISSN号	0035-8711
英文摘要	The statistical mechanics of isolated collisionless self-gravitating systems is a long-held puzzle, which has not been successfully resolved for nearly 50 years. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the first-order variation of the entropy, subject to the usual mass- and energy-conservation constraints, we obtain an entropy stationary equation. Incorporated with the Jeans equation, and by specifying some functional form for the anisotropy parameter beta, we numerically solve the two equations, and demonstrate that the velocity anisotropy parameter plays an important role in attaining a density profile that is finite in mass, energy and spatial extent. If incorporated again with some empirical density profile from simulations, our theoretical predictions of the anisotropy parameter, and the radial pseudo-phase-space density /Sigma 3(r) in the outer non-gravitationally degenerate region of the dark matter halo, agree rather well with the simulation data, and the predictions are also acceptable in the middle weak-degenerate region of the dark halo. The disagreements occur just in the inner strong-degenerate region because of the neglect of gravitational degeneracy. As far as we know, our results may be the first theoretical predictions based on the entropy principle that can partially match the empirical data. The second-order variational calculus reveals the seemingly paradoxical but actually complementary consequence that the equilibrium state of self-gravitating systems is the global minimum entropy state for the whole system under long-range violent relaxation, but simultaneously the local maximum entropy state for every and any small part of the system under short-range two-body relaxation and Landau damping. This minimum-maximum entropy duality means that the standard second law of thermodynamics needs to be re-expressed or generalized for self-gravitating systems. We believe that our findings, especially the complementary second law of thermodynamics, may provide crucial clues to the development of the statistical physics of self-gravitating systems as well as other long-range interaction systems.
学科主题	Physics
URL标识	查看原文
WOS记录号	WOS:000280672600044
公开日期	2012-08-02
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/5061]
专题	理论物理研究所_理论物理所1978-2010年知识产出
通讯作者	He, P , Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	He, Ping,Kang, Dong-Biao,He, P , Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China. Entropy principle and complementary second law of thermodynamics for self-gravitating systems[J]. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,2010,406(4):2678-2688.
APA	He, Ping,Kang, Dong-Biao,&He, P , Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China.(2010).Entropy principle and complementary second law of thermodynamics for self-gravitating systems.MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,406(4),2678-2688.
MLA	He, Ping,et al."Entropy principle and complementary second law of thermodynamics for self-gravitating systems".MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 406.4(2010):2678-2688.