金属中自由电子气体的非广延统计研究

采用分解近似的方法讨论了在Tsallis量子统计物理框架中，金属中自由电子气体的非广延参数q的热力学统计处理，计算出了总粒子数、总能量、自由能、热容量等热力学量，得出结论：在低温区域，q→1时，所有结果都可以回到传统的Fermi-Dirac分布，非广延参数q控制着系统的非广延程度.最后，详细讨论了q与热容量之间的关系，并与以前的结果作了比较. 关键词： Tsallis广义统计 非广延参数q 自由电子气体 Fermi-Dirac分布     

谐振势阱中旋转广义玻色系统的热力学性质

以非广延Tsallis统计理论为基础,导出了广义玻色-爱因斯坦统计分布表达式,并用其分别讨论了三维和二维谐振势阱约束的旋转广义玻色气体的热力学性质.结合系统粒子数、玻色-爱因斯坦凝聚(BEC)临界温度、基态粒子占据率和比热等物理量的解析表达式,分析了非广延参数和势阱旋转频率等因素对系统热力学性质的影响.     

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。     

非广延反应扩散系统的广义主方程

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出.与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性.当新的方程应用到单分子反应模型时, 非广延性对系统的稳定性将产生重要的作用, 特别是当系统接近临界状态时. 关键词： 主方程 非广延反应扩散系统 涨落     

基于二维最小Tsallis交叉熵的图像阈值分割方法

利用Tsallis熵的非广延性,提出了二维最小Tsallis交叉熵阈值分割方法.首先给出了二维Tsallis交叉熵的定义,并以最小二维Tsallis交叉熵为准则,利用粒子群优化算法来搜索最优二维阈值向量.该方法不仅进一步考虑了像素之间的空间邻域信息,而且考虑了目标和背景之间的相互关系,其分割性能优于基于Shannon熵的交叉熵阈值法和一维最小Tsallis交叉熵阈值法,并且具有很强的抗噪声能力.实验结果表明,该方法可以实现快速、准确的分割. 关键词： Tsallis交叉熵 二维直方图 粒子群优化算法 图像分割     

磁场中非广延相对论费米系统的统计性质

基于广义外势中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的热力学性质,给出总能、热容量、化学势的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统热力学性质的影响机理.研究显示,非广延参数不仅对热力学性质有直接的影响,而且也影响着磁场的物理效应. 随温度的升高,非广延参数及磁场对热力学性质的影响均被放大.极端相对论效应对化学势及热容量有特别显著的影响.     

具有非广延分布电子的碰撞等离子体磁鞘的结构

很多关于等离子体鞘层的研究工作都是基于电子满足经典的麦克斯韦速度分布函数,而等离子体中的粒子具有长程电磁相互作用,使用Tsallis提出的非广延分布来描述电子更为恰当.本文建立一个具有非广延分布电子的碰撞等离子体磁鞘模型,理论推导出受非广延参数q影响的玻姆判据,离子马赫数的下限数值会随着参数q的增大而减小.经过数值模拟,发现与具有麦克斯韦分布(q=1)电子的碰撞等离子体磁鞘对比,具有超广延分布(q<1)和亚广延分布(q>1)电子的碰撞等离子体磁鞘的结构各有不同,包括空间电势分布、离子电子密度分布、空间电荷密度分布.模拟结果显示非广延分布的参数q对碰撞等离子体磁鞘的结构具有不可忽略的影响.希望这些结论对相关的天体物理、等离子体边界问题的研究有参考价值.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

非汉字符号=TdS的导出方法及其前提假定

在绝对温度的确定、熵的存在及ｄＱ＝ＴｄＳ的导出等问题上向来就存在着两种热力学方法．其一是采用卡诺循环的传统方法，该法普遍适用于具有广延熵和非广延熵的系统；其二是分析方法，该法只适用于具有广延熵的系统．这是长期以来尚未解决的难题．本文旨在给出解决该难题的新的分析方法及其一种可能解．     

由完全开放系统的统计分布研究几个热力学系统

由完全开放系统的统计分布(也称N-E-V分布)计算了几个热力学系统的热力学量,其结果是与其他分布相同的,只是由平均值代替了固定不变值,但计算的相对涨落却是与通常理论完全不同的.通常的分布计算的相对涨落虽然不完全相同,但都正比于1/N,而由完全开放系统的统计分布计算的相对涨落却正比于1.     

Nonextensive statistical effects in protoneutron stars

We investigate the bulk properties of protoneutron stars in the framework of a relativistic mean-field theory based on nonextensive statistical mechanics, characterized by power-law quantum distributions. We study the relevance of nonextensive statistical effects on the b \beta -stable equation of state at fixed entropy per baryon, in the presence and in the absence of trapped neutrinos, for nucleonic and hyperonic matter. We show that nonextensive statistical effects could play a crucial role in the structure and in the evolution of the protoneutron stars also for small deviations from the standard Boltzmann-Gibbs statistics.     

Nonextensive statistics and incomplete information

We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying properties with the conventional normalization and the escort probability. These theoretical difficulties may be avoided by introducing an so called incomplete normalization allowing to deduce Tsallis' generalized distribution in a more convincing and consistent way. Received 29 October 2001 and Received in final form 30 January 2002     

Nonextensive thermostatistics and the H theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis." For q>0, the q-transport equation satisfies an H theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.     

Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Self-consistency in nonextensive statistical mechanics is studied as a recourse to parameter transformation, where different nonextensive parameters are presented for various theoretical branches. The unification between the first and third choices of the average definition and that between the normal and escort distributions are both examined. The problem of parameter inversion in the generalized H theorem is also investigated. The inconsistency between the statistical ensemble pressure and molecular dynamics pressure can be eliminated. This work also verifies the equivalence of physical temperature and gravitational temperature in nonextensive statistical mechanics. In these parameter transformations, the Tsallis entropy form is observed to remain invariant.     

Regge theory and statistical mechanics

An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee–Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non-trivial application to spin glass theory is shortly outlined.     

Nonextensive statistical mechanics of ionic solutions

Classical mean-field Poisson–Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson–Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye–Hückel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q.     

Inherent correlations between thermodynamics and statistical physics in extensive and nonextensive systems

With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistical physics. These relations are proved through the MaxEnt approach once again. It is found that for a reversible isothermal process, the information contained in the first and second laws of thermodynamics and the MaxEnt approach is equivalent. Moreover, these relations are used to derive the probability distribution functions in nonextensive and extensive statistics and calculate the generalized forces of some interesting systems. The results obtained are of universal significance.     

Nonextensive statistical mechanics of q-bosons based on the q-deformed entropy

Based on the q ↔ q⁻¹ symmetric deformed entropy, we develop a general framework for nonextensive statistical mechanics of ensembles of q-deformed systems. Applying this doubly deformed formalism to q-bosons, a correction to the Planck law is evaluated in the weak deformation regime and its properties are discussed. It is found that at high temperature the dominant part of the correction comes from the deformation of the oscillator dynamics, whereas at low temperature the deformation of the entropy gives a leading contribution. This suggests the nonextensive approach to q-deformed ensembles might be important at low temperature.     

Nonextensive nuclear liquid–gas phase transition

We study an effective relativistic mean-field model of nuclear matter with arbitrary proton fraction at finite temperature in the framework of nonextensive statistical mechanics, characterized by power-law quantum distributions. We investigate the presence of thermodynamic instability in a warm and asymmetric nuclear medium and study the consequent nuclear liquid–gas phase transition by requiring the Gibbs conditions on the global conservation of baryon number and electric charge fraction. We show that nonextensive statistical effects play a crucial role in the equation of state and in the formation of mixed phase also for small deviations from the standard Boltzmann–Gibbs statistics.     

Stability of incomplete entropy and incomplete expectation

Based on the principle of maximum entropy, the q-exponential distribution can be derived from several different nonextensive entropies including the incomplete entropy. It is widely used in nonextensive statistical mechanics. In the present paper, it is shown that the incomplete expectation value and incomplete entropy are stable under small deformation of the probability distribution function of the system.