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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.

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.

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

其中<math>k_B</math>是玻尔兹曼常数，<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.

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.

量子统计力学是应用于量子力学系统的统计力学。在量子力学中，系综（可能量子态的概率分布）由密度算符S来描述，它是一个描述量子系统希尔伯特空间 H 上的非负的、自伴随的、迹1的迹类算符。这可以在量子力学的不同数学形式上来表示。量子逻辑就是这样一种形式。

量子统计力学是应用于量子力学系统的统计力学。在量子力学中，系综（可能量子态的概率分布）由密度算符S来描述，它是一个描述量子系统希尔伯特空间 H 上的非负的、自伴随的、迹为1的迹类算符。这可以在量子力学的不同数学形式上来表示。量子逻辑就是这样一种形式。

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、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。

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、列夫·朗道、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。