对有关涨落的准热力学理论中一个问题的讨论

本文讨论了涨落的准热力学理论中一个在教学中令人困扰的问题，简要地阐述了为什么在这里热力学的基本方程式对系统不适用，而对外界（热源）又适用的道理，并说明了涨落的准热力学理论是一种近似的理论．     

统计分布的统一形式

采用量大熵原理作为统计力学基本假设，简洁地导出系统微观态的概率分布，引入一套符号规定，将众多形式的统计分布，热力学公式、涨落公式归纳为极易掌握和记忆的统一形式。     

论广义力的涨落

应用系统理论和准热力学方法，计算了气体压强和电介质极化强度的涨落。结果表明，这两个量在正则系统和巨正则系统的涨落均在数值上的差异，准热力学方法对气体压强的涨落给出的结果和巨正则系综相同，对电介质极化强度的涨落所得结果则和正则系缩相同，文中阐明了这些结果异同的原因。     

压强的微观表达式-((H)/(V))_(qp)及其涨落

按照系综理论，压强ｐ是偏导数－（　Ｈ／ Ｖ）ｑｐ的统计平均值：ｐ＝〈－Ｈ／Ｖ）ｑｐ〉，人们由它引出结论：－（Ｈ／Ｖ）ｑｐ作为一个相函数乃是压强的瞬时值，但根据这一前提得到的压强涨落公式与准热力学理论矛盾，并引起了长期的争论．本文提出如下见解：偏导数－（Ｈ／Ｖ）ｑｐ与相变量（ｑ，ｐ）的选择有关，只有对于某种特殊的相变量，它才能表示压强的瞬时值．这时公式〈（２Ｈ／ Ｖ２）ｑｐ〉＝（ｐ／Ｖ）ｓ成立．而根据这一公式，可以从系综理论的压强涨落公式过渡到准热力学理论的压强涨落公式．     

金属纳米晶体的界面热力学特性

根据准协德拜近似从理论上计算了金属纳米晶体的界面热力学特性,包括界面过剩能、过剩焓、过剩熵、过剩Gibbs自由能等,着重讨论了界面过剩热力学参量与界面过剩体积和温度的关系.一些实验测量结果表明,理论计算与实验结果基本相符. 关键词：     

系统理论和涨落的准热力学理论

讨论了系综理论和涨落的准热力学理论两者之间的联系和差别，进一步明确了它们不等效的。     

系综理论和涨落的准热力学理论

讨论了系综理论和涨落的准热力学理论两者之间的联系和差别，进一步明确了它们是不等效的．     

光学耗散系统的准热力学模型及其在光学双稳性相变问题上的应用

本文以光学耗散系统为范例,论证在满足细致平衡原理的条件下,可以与传统热力学相平行地发展一种“准热力学”模型。然后运用此模型系统而普遍地讨论了光学双稳系统的临界现象与相变。又借助Ginzburg-Landau模型处理了光学双稳性(第二类)临界点附近的涨落与关联。将平衡热力学的Landau相变理论推广到具有双稳性并远离热平衡的耗散系统。     

小系统：热力学何时适用

本文对受激核的热力学描述做了基本的分析． 根据测不准关系与涨落概念，采用核的核子气模型， 给出了在定量使用温度和熵概念时，该小系统粒子数 的限制条件．     

关于准热力学理论的几点看法

关于围绕平均值的涨落存在着两种理论,一种是用系综分布函数计算涨落,称为系综理论,一种是认为热力学基本方程在偏离平均值时也成立,用它和玻尔兹曼关系来计算涨落的准热力学理论.这两种理论有无关系?国内几本教科书的讲法,大体有以下几种情况:1.完全没触及;2.仅仅指出一些量的涨落值,两种理论得到的结果相同,未作进一步的结论; 3.认为两种几率表达式只是不同的表现形式,即认为两种理论应有完全相同的结果;4.认为只有对于某些量(能量和粒子数)的涨落计算,才能得到相同的结果.我们觉得对于处理同一问题的几种理论作出评价,搞清它们之间的关系…     

Entropy bounds and Cardy–Verlinde formula in Yang–Mills theory

Using gauge formulation of gravity the three-dimensional SU(2) YM theory equations of motion are presented in equivalent form as FRW cosmological equations. With the radiation, the particular (periodic, big bang – big crunch) three-dimensional universe is constructed. Cosmological entropy bounds (so-called Cardy–Verlinde formula) have the standard form in such universe. Mapping such universe back to YM formulation we got the thermal solution of YM theory. The corresponding holographic entropy bounds (Cardy–Verlinde formula) in YM theory are constructed. This indicates to universal character of holographic relations.     

Universality and a generalized C-function in CFTs with AdS duals

We argue that the thermodynamics of conformal field theories with AdS duals exhibits a remarkable universality. At strong coupling, a Cardy–Verlinde entropy formula holds even when R-charges or bulk supergravity scalars are turned on. In such a setting, the Casimir entropy can be identified with a generalized C-function that changes monotonically with temperature as well as when non-trivial bulk scalar fields are introduced. We generalize the Cardy–Verlinde formula to cases where no subextensive part of the energy is present and further observe that such a formula is valid for the super Yang–Mills theory in D=4 even at weak coupling. Finally we show that a generalized Cardy–Verlinde formula holds for asymptotically flat black holes in any dimension.     

Entropy of nonrotating isolated horizons in Lovelock theory from loop quantum gravity

In this paper,the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory.The final entropy matches the Wald entropy formula for this theory.We also confirm the conclusion obtained by Bodendorfer et al.that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.     

Cardy-Verlinde Formula and Thermodynamics of Dilaton-axion Black Hole

In this paper, we have shown that the entropy of the dilaton-axion black hole can be expressed by the Cardy-Verlinde formula. The later is supposed to be an entropy formula of conformal field theory in any dimension. Next we have calculated the first order correction to the Cardy-Verlinde formula in the context of dilaton-axion black hole.     

无相互作用费米量子信道直积态容量研究

用费米线性光学方法,提出无相互作用费米量子信道物理模型.用平稳量子高斯态协方差矩阵性质及Majorization不等式理论,推导出在平稳高斯输入态下费米量子信道最小输出熵的表达式.利用在n模费米系统添加一个额外模的方法,得到平稳高斯态和高斯态输出熵的关系|利用此关系式,借助在高斯输入态下费米信道最小输出熵值是可达的猜测,推导出无相互作用费米信道直积态容量的表达式.最后,用最小输出熵的迭代算法验证已推出的费米信道最小输出熵表达式正确性,数值计算结果表明:对于带噪声的无相互作用费米量子信道,已推出最小输出熵与数值计算结果的吻合度可以达到10e-9.     

Cardy-Verlinde Formula of?Kehagias-Sfetsos Black Hole

In this paper, we have shown that the entropy of the Kehagias-Sfetsos black hole in Hořava-Lifshitz (HL) gravity can be expressed by the Cardy-Verlinde formula. The later is supposed to be an entropy formula of conformal field theory in any dimension.     

Universality of entropy scaling in one dimensional gapless models

We consider critical models in one dimension. We study the ground state in the thermodynamic limit (infinite lattice). We are interested in an entropy of a subsystem. We calculate the entropy of a part of the ground state from a space interval (0,x). At zero temperature it describes the entanglement of the part of the ground state from this interval with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at any temperature. At zero temperature our formula reproduces a logarithmic formula, discovered by Vidal, Latorre, Rico, and Kitaev for spin chains. We prove our formula by means of conformal field theory and the second law of thermodynamics. Our formula is universal. We illustrate it for a Bose gas with a delta interaction and for the Hubbard model.     

Asymptotic structure near event horizon and Cardy-Verlinde formula for general asymptotically flat stationary black hole

The asymptotically anti-de Sitter structure near event horizon of general asymptotically flat stationary black hole is found, and the Cardy-Verlinde formula is generalized to the asymptotically flat black holes in the Einstein-Maxwell theory and low-energy effective field theory describing string. The result that the entropy of conformal field theory (CFT) agrees precisely with black-hole entropy provides a CFT interpretation of the Bekenstein-Hawking entropy of the asymptotically flat stationary black holes.     

An Entropy Functional for Riemann-Cartan Space-Times

By viewing space-time as a continuum elastic medium and introducing an entropy functional for its elastic deformations, T. Padmanabhan has shown that general relativity emerges from varying the functional and that the latter suggests holography for gravity and yields the Bekenstein-Hawking entropy formula. In this paper we extend this idea to Riemann-Cartan space-times by constructing an entropy functional for the elastic deformations of space-times with torsion. We show that varying this generalized entropy functional permits to recover the full set of field equations of the Cartan-Sciama-Kibble theory. Our generalized functional shows that the contributions to the on-shell entropy of a bulk region in Riemann-Cartan space-times come from the boundary as well as the bulk and hence does not suggest that holography would also apply for gravity with spin in space-times with torsion. It is nevertheless shown that for the specific cases of Dirac fields and spin fluids the system does become holographic. The entropy of a black hole with spin is evaluated and found to be in agreement with Bekenstein-Hawking formula.     

Logarithmic correction to BMSFT entanglement entropy

Using Rindler method we derive the logarithmic correction to the entanglement entropy of a two dimensional BMS-invariant field theory (BMSFT). In particular, we present a general formula for extraction of the logarithmic corrections to both the thermal and the entanglement entropies. We also present a CFT formula related to the logarithmic correction of the BTZ inner horizon entropy which results in our formula after taking appropriate limit.