统计物理

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Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neuroscience, and even some social sciences, such as sociology and linguistics. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.

Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neuroscience, and even some social sciences, such as sociology and linguistics. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.

统计物理学是物理学的一个分支，它使用概率论和统计学的方法，特别是数学工具来处理大量的人口和近似法，来解决物理问题。它可以描述具有内在随机性的广泛领域。它的应用领域包括物理学、生物学、化学、神经科学，甚至社会学、语言学等一些社会科学领域的许多问题。它的主要目的是用控制原子运动的物理定律来阐明聚合物质的性质。

In particular, statistical mechanics develops the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.

In particular, statistical mechanics develops the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.

特别是，统计力学从对潜在的微观系统的概率检验中发展了热力学的现象学结果。历史上，统计学方法应用于物理学的第一个主题是力学领域，它涉及到粒子或物体在受力时的运动。

Statistical mechanics

统计力学

Main article: Statistical mechanics

Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics, classical mechanics, and quantum mechanics at the microscopic level. Because of this history, statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics.

Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics, classical mechanics, and quantum mechanics at the microscopic level. Because of this history, statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics.

统计力学提供了一个框架，将单个原子和分子的微观属性与日常生活中可以观察到的物质的宏观或体积属性联系起来，从而在微观层面上解释了热力学作为统计、经典力学和量子力学的自然结果。由于这段历史，统计物理学常常被认为是统计力学或统计热力学的同义词。

One of the most important equations in statistical mechanics (akin to [math]\displaystyle{ F=ma }[/math] in Newtonian mechanics, or the Schrödinger equation in quantum mechanics) is the definition of the partition function [math]\displaystyle{ Z }[/math], which is essentially a weighted sum of all possible states [math]\displaystyle{ q }[/math] available to a system.

One of the most important equations in statistical mechanics (akin to [math]\displaystyle{ F=ma }[/math] in Newtonian mechanics, or the Schrödinger equation in quantum mechanics) is the definition of the partition function [math]\displaystyle{ Z }[/math], which is essentially a weighted sum of all possible states [math]\displaystyle{ q }[/math] available to a system.

统计力学最重要的方程之一(类似于牛顿运动定律的数学 f ma / math，或者量子力学的薛定谔方程数学)是配分函数数学 z / math 的定义，它本质上是一个系统可用的所有可能状态数学 q / math 的加权和。

[math]\displaystyle{ Z = \sum_q \mathrm{e}^{-\frac{E(q)}{k_BT}} }[/math]

[math]\displaystyle{ Z = \sum_q \mathrm{e}^{-\frac{E(q)}{k_BT}} }[/math]

数学 z sum q mathrum { e } ^ {- frac { e (q)}{ k bt } / math

where [math]\displaystyle{ k_B }[/math] is the Boltzmann constant, [math]\displaystyle{ T }[/math] is temperature and [math]\displaystyle{ E(q) }[/math] is energy of state [math]\displaystyle{ q }[/math]. Furthermore, the probability of a given state, [math]\displaystyle{ q }[/math], occurring is given by

where [math]\displaystyle{ k_B }[/math] is the Boltzmann constant, [math]\displaystyle{ T }[/math] is temperature and [math]\displaystyle{ E(q) }[/math] is energy of state [math]\displaystyle{ q }[/math]. Furthermore, the probability of a given state, [math]\displaystyle{ q }[/math], occurring is given by

其中 math k b / math 是波兹曼常数，math t / math 是温度，math e (q) / math 是状态数学的能量。此外，给定状态(math q / math)发生的概率由

[math]\displaystyle{ P(q) = \frac{ {\mathrm{e}^{-\frac{E(q)}{k_BT}}}}{Z} }[/math]

[math]\displaystyle{ P(q) = \frac{ {\mathrm{e}^{-\frac{E(q)}{k_BT}}}}{Z} }[/math]

数学 p (q) frac { e } ^ {- frac { e (q)}{ k bt }}}{ z } / math

Here we see that very-high-energy states have little probability of occurring, a result that is consistent with intuition.

Here we see that very-high-energy states have little probability of occurring, a result that is consistent with intuition.

这里我们看到，极高能量状态发生的可能性很小，这个结果与直觉是一致的。

A statistical approach can work well in classical systems when the number of degrees of freedom (and so the number of variables) is so large that the exact solution is not possible, or not really useful. Statistical mechanics can also describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics (particularly at high Knudsen numbers), or plasma physics.

A statistical approach can work well in classical systems when the number of degrees of freedom (and so the number of variables) is so large that the exact solution is not possible, or not really useful. Statistical mechanics can also describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics (particularly at high Knudsen numbers), or plasma physics.

在经典系统中，当自由度数目(以及变量数目)很大时，统计方法可以很好地工作，以至于精确解是不可能的，或者不是真正有用。统计力学还可以描述非线性动力学、混沌理论、热物理学、流体动力学(特别是在高努森数时)或等离子体物理学中的工作。

Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions. A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the properties of a complex system.

Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions. A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the properties of a complex system.

虽然统计物理学中的一些问题可以用近似和展开来解析地解决，但目前的大多数研究利用现代计算机的巨大处理能力来模拟或近似解。处理统计问题的一个常用方法是使用蒙特卡罗模拟来洞察复杂系统的性质。

Quantum statistical mechanics

量子统计力学

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.

量子统计力学统计力学应用于量子力学系统。在量子力学中，描述系综的密度算符 s 是描述量子系统的希尔伯特空间 h 上迹1的一个非负的、自伴随的迹类算符，称为密度算符 s。这可以用不同的数学公式表示出来，这些公式可以用不同的量子力学来表示。量子逻辑就是这样一种形式。

Scientists and universities

科学家和大学

A significant contribution (at different times) in development of statistical physics was given by Satyendra Nath Bose, James Clerk Maxwell, Ludwig Boltzmann, J. Willard Gibbs, Marian Smoluchowski, Albert Einstein, Enrico Fermi, Richard Feynman, Lev Landau, Vladimir Fock, Werner Heisenberg, Nikolay Bogolyubov, Benjamin Widom, Lars Onsager, Benjamin and Jeremy Chubb (also inventors of the titanium sublimation pump), Humb, Manoo, and others. Statistical physics is studied in the nuclear center at Los Alamos. Also, Pentagon has organized a large department for the study of turbulence at Princeton University. Work in this area is also being conducted by Saclay (Paris), Max Planck Institute, Netherlands Institute for Atomic and Molecular Physics and other research centers.

A significant contribution (at different times) in development of statistical physics was given by Satyendra Nath Bose, James Clerk Maxwell, Ludwig Boltzmann, J. Willard Gibbs, Marian Smoluchowski, Albert Einstein, Enrico Fermi, Richard Feynman, Lev Landau, Vladimir Fock, Werner Heisenberg, Nikolay Bogolyubov, Benjamin Widom, Lars Onsager, Benjamin and Jeremy Chubb (also inventors of the titanium sublimation pump), Humb, Manoo, and others. Statistical physics is studied in the nuclear center at Los Alamos. Also, Pentagon has organized a large department for the study of turbulence at Princeton University. Work in this area is also being conducted by Saclay (Paris), Max Planck Institute, Netherlands Institute for Atomic and Molecular Physics and other research centers.

萨特延德拉·纳特·玻色、詹姆斯·克拉克·麦克斯韦、路德维希·玻尔兹曼、 j. Willard Gibbs、马利安·斯莫鲁霍夫斯基、 Albert Einstein、 Enrico Fermi、 Richard Feynman、 Lev Landau、 Vladimir Fock、维尔纳·海森堡、尼古拉·博戈柳博夫、 Benjamin Widom、 Lars Onsager、 Benjamin 和 Jeremy Chubb (也是钛升华泵的发明者)、 Humb、 Manoo 等人对统计物理学的发展做出了重大贡献。统计物理学在洛斯阿拉莫斯的核中心研究。此外，五角大楼已经在普林斯顿大学组织了一个大的部门来研究湍流。萨克雷(巴黎)、马克斯 · 普朗克研究所、荷兰原子与分子物理研究所和其他研究中心也在进行这方面的工作。

Achievements

成就

Statistical physics allowed us to explain and quantitatively describe superconductivity, superfluidity, turbulence, phlogistine, antiphlogistine, ludige, collective phenomena in solids and plasma, and the structural features of liquid. It underlies the modern astrophysics. It is statistical physics that helped us to create such intensively developing study of liquid crystals and to construct a theory of phase transition and critical phenomena. Many experimental studies of matter are entirely based on the statistical description of a system. These include the scattering of cold neutrons, X-ray, visible light, and more.

Statistical physics allowed us to explain and quantitatively describe superconductivity, superfluidity, turbulence, phlogistine, antiphlogistine, ludige, collective phenomena in solids and plasma, and the structural features of liquid. It underlies the modern astrophysics. It is statistical physics that helped us to create such intensively developing study of liquid crystals and to construct a theory of phase transition and critical phenomena. Many experimental studies of matter are entirely based on the statistical description of a system. These include the scattering of cold neutrons, X-ray, visible light, and more.

统计物理学使我们能够解释和定量描述超导现象、超流动性、湍流、燃素、抗燃素、络合物、固体和等离子体中的集体现象以及液体的结构特征。它是现代天体物理学的基础。正是统计物理学帮助我们开展了如此深入的液晶研究，并建立了相变和临界现象的理论。许多物质的实验研究完全基于对系统的统计描述。这些包括冷中子、 x 射线、可见光等的散射。

Statistical physics plays a major role in Physics of Solid State Physics, Materials Science, Nuclear Physics, Astrophysics, Chemistry, Biology and Medicine (e.g. study of the spread of infectious diseases), Information Theory and Technique but also in those areas of technology owing to their development in the evolution of Modern Physics. It still has important applications in theoretical sciences such as Sociology and Linguistics and is useful for researchers in higher education, corporate governance, and industry.

Statistical physics plays a major role in Physics of Solid State Physics, Materials Science, Nuclear Physics, Astrophysics, Chemistry, Biology and Medicine (e.g. study of the spread of infectious diseases), Information Theory and Technique but also in those areas of technology owing to their development in the evolution of Modern Physics. It still has important applications in theoretical sciences such as Sociology and Linguistics and is useful for researchers in higher education, corporate governance, and industry.

统计物理学在固体物理学、材料科学、核物理学、天体物理学、化学、生物学和医学等学科中占有重要地位。研究传染病的传播) ，信息理论和技术，但也在这些领域的技术，由于他们的发展，在现代物理学的演变。它在社会学和语言学等理论科学中仍有重要应用，对高等教育、公司治理和工业领域的研究人员也很有用。

See also

参见

• Statistical ensemble

• Statistical field theory

• Mean sojourn time

• Dynamics of Markovian particles

• Complex network

• Mathematical physics

• Combinatorics and physics

• Binomial distribution

Notes

注释

References

参考资料

Further reading

进一步阅读

• Fundamentals of Statistical and Thermal Physics by Frederick Reif

Thermal and Statistical Physics (lecture notes, Web draft 2001) by Mallett M., Blumler P.

Thermal and Statistical Physics (lecture notes, Web draft 2001) by Mallett M., Blumler P.

[ http://librarum.org/book/4456/1热力学和统计物理学(讲义，Web draft 2001)]作者: Mallett m. Blumler p。

• BASICS OF STATISTICAL PHYSICS: Second Edition

by Harald J W Müller-Kirsten (University of Kaiserslautern, Germany)

by Harald J W Müller-Kirsten (University of Kaiserslautern, Germany)

作者: Harald j w m ller-kirsten (德国凯泽斯劳滕大学)

• Statistical Physics and other resources by Leo P Kadanoff

• Statistical Physics - Statics, Dynamics and Renormalization by Leo P Kadanoff

• History and outlook of statistical physics by Dieter Flamm

! ——收藏

Category:Statistical physics

分类: 统计物理学

Category:Formal sciences

类别: 正规科学

This page was moved from wikipedia:en:Statistical physics. Its edit history can be viewed at 统计物理/edithistory