Thermodynamical Properties of Quark-Gluon Plasma and Effects of Bulk Viscosity

In this paper, we use equation of state, temperature and bulk viscosity of the quark gluon plasma and calculate some cosmological and thermodynamical quantities. In order to obtain such quantities we choose special case of energy density in terms of Hubble parameter. We apply the approximation solution and obtain the exact form of scale factor, temperature and bulk viscous stress. Finally, we draw some figures for the geometric and thermodynamic quantities in terms of time.     

含非线性微扰项的二阶动力学系统的一阶近似守恒量的一种新求法

从一阶近似守恒量的性质出发,把受微扰系统视为未受微扰系统与微扰项的迭加,提出一种分三步求得一阶近似守恒量的新方法:先选择合适的方法求得未受微扰系统的守恒量I0,再考虑微扰项对守恒量I0的影响,最后利用一阶近似守恒量的性质求得一阶近似守恒量.用该方法研究了一实际的受非线性微扰作用的两自由度动力学系统,得到4个稳定的一阶近似守恒量.用坐标变换法和微扰法得到系统一阶近似解的表达式,并讨论4种特殊情况下的一阶近似解.     

一类多自由度线性耦合系统的对称性与守恒量研究

运用改变坐标标度和旋转坐标轴的方法先消去Lagrange函数中的耦合项，直接得到新坐标系下的守恒量，利用坐标反变换得到原坐标系下的守恒量，并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性，最后举例说明结果的应用. 关键词： 多自由度线性耦合系统 守恒量 Noether对称性 Lie对称性     

Statistical Analysis of STU Black Holes

In this paper we consider STU black hole and calculate statistical quantities. We analyze some important quantities such as free energy, specific heat, and partition function numerically. We compare thermodynamics entropy with statistics entropy and find agreement between them.     

奇异 Chetaev型非完整系统Nielsen方程的Lie-Mei对称性与守恒量

研究奇异Chetaev型非完整系统Nielsen方程的Lie-Mei对称性, 建立系统Nielsen方程的Lie-Mei对称性方程, 给出系统Nielsen方程强Lie-Mei对称性和弱Lie-Mei对称性的定义, 得到对称性导致的Hojman守恒量和Mei守恒量, 最后给出说明性算例. 关键词： 奇异非完整系统 Nielsen方程 Lie-Mei对称性 守恒量     

Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomicdynamicM systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equationsand restrictive equations and give three definitions of Lie symmetries before the structure equations and conservedquantities of tile Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example ispresented for illustrating the results.     

一类非完整奇异系统的Lie对称性与守恒量

利用微分方程在无限小变换群下的不变性,研究一类非完整奇异系统的Lie对称性.给出Lie对称性的确定方程、限制方程、附加限制方程和结构方程,并给出守恒量的形式 关键词： 奇异系统 非完整约束 Lie对称性 守恒量     

Macroscopic Equations for a Multicomponent Plasma

From the balance equations for partial quantities we derive equations for lumped quantities, e.g. a generalized Ohm's law. They are especially useful for a three-component system (electrons, one species of ions and neutral particles). Certain conditions are derived and investigated to describe a plasma with more than three components by the lumped quantities.     

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.     

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems.Firstly,we give the definition of integrating factors for the differential equations of motion of a mechanical system.Next,the necessary conditions for the existemce of the conserved quantities are studied in detail.Then,we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system.Finally,an exampled is given to illustrate the application of the result.     

Lie symmetries and conserved quantities of non—holonomic mechanical systems with unilateral Vacco constraints

In this paper,we study the Lie symmetries and the conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints.we give the conditions and the form of conserved quantities due to the Lie symmetries of the systems,and present the inverse problem of the above proble,i.e.finding the corresponding Lie symmetry transformation according to a given integral of the system.Finally,we give an example to illustrate the application of the results.     

Informational properties of holographic Lifshitz field theory

In this paper,we explore the properties of holographic entanglement entropy(HEE),mutual information(MI) and entanglement of purification(EoP) in holographic Lifshitz theory.These informational quantities exhibit some universal properties of holographic dual field theory.For most configuration parameters and temperatures,these informational quantities change monotonically with the Lifshitz dynamical critical exponent z.However,we also observe some non-monotonic behaviors for these informational quantities in some specific spaces of configuration parameters and temperatures.A particularly interesting phenomenon is that a dome-shaped diagram emerges in the behavior of MI vs z,and correspondingly a trapezoid-shaped profile appears in that of EoP vs z.This means that for some specific configuration parameters and temperatures,the system measured in terms of MI and EoP is entangled only in a certain intermediate range of z.     

Lattice QCD calculations for the physical equation of state

In this report we consider the numerical simulations at finite temperature using lattice QCD data for the computation of the thermodynamical quantities including the pressure, energy density and the entropy density. These physical quantities can be related to the equation of state for quarks and gluons. We shall apply the lattice data to the evaluation of the specific structure of the gluon and quark condensates at finite temperature in relation to the deconfinement and chiral phase transitions. Finally we mention the quantum nature of the phases at lower temperatures.     

Entanglement of a two-level atom papered in a finite trio-coherent state

In this paper, we study the interaction between an effective two-level atom and a three-mode field. The atom and the field are initially in the excited state and finite dimensional trio-coherent state, respectively. For this sytem, we investigate the atomic inversion, the von Neumann entropy, and the atomic Wehrl entropy. We show that there is a connection between all of these quantities. Also, we prove that the atomic Wehrl entropy exhibits a temporal evolution similar to the von Neumann entropy. It is observed that the Stark shift parameter plays an important role on the evolution of these quantities.     

Thermodynamic stability of black holes surrounded by quintessence

We study the thermodynamic stabilities of uncharged and charged black holes surrounded by quintessence (BHQ) by means of effective thermodynamic quantities. When the state parameter of quintessence \(\omega _q\) is appropriately chosen, the structures of BHQ are something like that of black holes in de Sitter space. Constructing the effective first law of thermodynamics in two different ways, we can derive the effective thermodynamic quantities of BHQ. Especially, these effective thermodynamic quantities also satisfy Smarr-like formulae. It is found that the uncharged BHQ is always thermodynamically unstable due to negative heat capacity, while for the charged BHQ there are phase transitions of the second order. We also show that there are several differences on the thermodynamic properties and critical behaviors of BHQ between the two ways we employed.     

广义非完整力学系统的Lie对称性与Noether守恒量

研究广义非完整力学系统的Lie对称性与Noether守恒量,建立Lie对称性的确定方程、限制方程和附加限制方程,给出结构方程和Noether守恒量的形式,研究Lie对称性的逆问题,并举算例说明结果的应用.     

非保守力和非完整约束对Hamilton系统Lie对称性的影响

研究非保守力和非完整约束对Hamilton系统的Lie对称性和守恒量的影响.分别研究了Hamilt on系统受到非保守力和非完整约束作用时，系统的Lie对称性保持不变的条件，同时给出了 系统的结构方程和守恒量保持不变的条件.以著名的Emden方程和Appell-Hamel模型为例进行 了分析讨论. 关键词： 分析力学 Hamilton系统 非保守力 非完整约束 对称性 守恒量     

Statistical geometry of hard sphere systems: exact relations for first-order phase transitions in multicomponent systems

Statistical geometry provides exact relations between the thermophysical properties of hard sphere systems and various geometric quantities. Utilizing recently derived relations that describe multicomponent hard sphere systems, we derive two new expressions which place rigorous constraints on the behaviour of geometric quantities across a first-order phase transition. Some implications of these constraints for a binary mixture of additive hard spheres are discussed.     

Thermodynamics of de Sitter Black Holes in Massive Gravity

In this paper, by taking de Sitter space-time as a thermodynamic system, we study the effective thermodynamic quantities of de Sitter black holes in massive gravity, and furthermore obtain the effective thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstr¨om-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the effective thermodynamic quantities and relevant parameters play a very important role in the investigation of the stability and evolution of de Sitter space-time.