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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.

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.

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.

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

One of the most important equations in statistical mechanics (akin to <math>F=ma</math> in Newtonian mechanics, or the Schrödinger equation in quantum mechanics) is the definition of the partition function <math>Z</math>, which is essentially a weighted sum of all possible states <math>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。

统计力学最重要的方程之一(类似于牛顿运动定律的<math>F=ma</math> ，或者量子力学的薛定谔方程)是配分函数 <math>Z</math> 的定义，它本质上是一个系统所有可能状态<math>q</math>的加权和。

where <math>k_B</math> is the Boltzmann constant, <math>T</math> is temperature and  <math>E(q)</math> is energy of state  <math>q</math>. Furthermore, the probability of a given state, <math>q</math>, occurring is given by

where <math>k_B</math> is the Boltzmann constant, <math>T</math> is temperature and  <math>E(q)</math> is energy of state  <math>q</math>. Furthermore, the probability of a given state, <math>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

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<math>q</math>的能量。此外，给定状态 <math>q</math>出现的概率是

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.

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。

在经典系统中，当自由度(以及变量数)很大以至于精确解是不可能的，或者不是真正有用时，统计方法可以很好地起作用。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(特别是在高克努森数时)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.

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.

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。

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、约西亚·威拉德·吉布斯、马利安·斯莫鲁霍夫斯基、阿尔伯特·爱因斯坦、恩里科·费米，理查德·费曼、列弗·兰道、弗拉基米尔·福克、维尔纳·海森堡、尼古拉·博戈柳博夫、本杰明·维多姆、昂萨格、本杰明和杰里米·丘布(也是钛升华泵的发明者)、亨伯、马诺等人在不同时期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被广泛研究。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。

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.