陈玲,张保成

• 1:中国地质大学(武汉)数学与物理学院

摘要(Abstract)：

一直以来大家都认为物理系统的热力学熵或统计熵与该系统所占的空间体积成正比,特别是微观体系的统计计算为这一结论提供了可信的基础。事实上,最近的研究发现,即使采用几乎同样的统计计算方法,当研究对象变成黑洞的时候,统计熵不再正比于体积,而是正比于面积。这样新颖而有趣的结论不仅对理解统计计算方法本身,而且对理解热力学量之间的关系都有极大的帮助。

关键词(KeyWords)： 统计熵;玻色体系;黑洞

Abstract:

Keywords:

基金项目(Foundation): 中央高校教改基金本科教学工程（2019G46）;; 国家自然科学基金（11654001,91636263）资助

作者(Author): 陈玲,张保成

参考文献(References)：

• [1]汪志诚．热力学与统计物理[M]．北京：高等教育出版社，2013.
• [2]杨展如．量子统计物理学[M]．北京：高等教育出版社，2012.
• [3] COWAN B.Topics in statistical mechanics[M]．上海：复旦大学出版社，2006.
• [4] DEBENEDICTIS A A.Developments in black hole research:Classical,semi-classical,and quantum[J].Nova Science Publisher,2008:371-426.
• [5] SOLODUKHIN S N.Entanglement entropy of black holes[J].Living Review in Relativity,2011,14:8.
• [6] FROLOV V P.Why the entropy of a black hole is A/4[J].Physical Review Letter,1995,74:3319.
• [7] CAI R G,CHEN C M,MAEDA K,et al.Entropy function and universality of entropy-area relation for small black holes[J].Physical Review D,2008,77:064030.
• [8] CHRISTODOULOU M,ROVELLI C.How big is a black hole?[J].Physical Review D,2015,91:064046.
• [9] ZHANG B C.Entropy in the interior of a black hole and thermodynamics[J].Physical Review D,2015,92:081501(R).
• [10] ZHANG B C,YOU L.Infinite volume of noncommutative black hole wrapped by finite surface[J].Physics Letters B,2017,765:226.
• [11] ZHANG B C.On the entropy associated with the interior of a black hole[J].Physics Letters B,2017,773:644.
• [12] MASSAR S.Semiclassical back reaction to black hole evaporation[J].Physical Review D,1995,52:5857.
• [13] BEKENSTEIN J D.Black Holes and Entropy[J].Physical Review D,1973,7:2333.
• [14] BARDEEN J M,CARTER B,HAWKING S W.The Four Laws of Black Hole Mechanics[J].Communications in Mathematical Physics,1973,31:161.
• [15] CANDELAS P.Vacuum polarization in Schwarzschild spacetime[J].Physical Review D,1980,21:2185.
• [16] ELSTER T.Vacuum polarization near a black hole creating particles[J].Physics Letters A,1983,94:205.