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| {{Expand French|Physique statistique|date=July 2012}}
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| '''Statistical physics''' is a branch of [[physics]] that uses methods of [[probability theory]] and [[statistics]], and particularly the [[Mathematics|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]], [[neurology]], and even some social sciences, such as [[sociology]]. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.<ref>{{cite book|title = Introduction to Statistical Physics |last = Huang |first = Kerson |year = |publisher= CRC Press| isbn = 978-1-4200-7902-9 |page=15 |edition = 2nd}}</ref>
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| In particular, [[statistical mechanics]] develops the [[Phenomenology (science)|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.
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| ==Statistical mechanics==
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| {{main|Statistical mechanics}}
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| [[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, the statistical physics is often considered synonymous with statistical mechanics or [[statistical thermodynamics]].<ref group=note>This article presents a broader sense of the definition of statistical physics</ref>
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| One of the most important equations in Statistical mechanics (analogous to <math>F=ma</math> in mechanics, or the [[Schroedinger equation|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.
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| : <math>Z = \sum_q \mathrm{e}^{-\frac{E(q)}{k_BT}}</math>
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| 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
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| : <math>P(q) = \frac{ {\mathrm{e}^{-\frac{E(q)}{k_BT}}}}{Z}</math>
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| Here we see that very-high-energy states have little probability of occurring, a result that is consistent with intuition.
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| A statistical approach can work well in classical systems when the number of [[degrees of freedom (physics and chemistry)|degrees of freedom]] (and so the number of variables) is so large that 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 number]]s), or [[plasma physics]].
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| 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 dynamics of a complex system.
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| ==See also==
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| * [[Statistical ensemble (mathematical physics)|Statistical ensemble]]
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| * [[Statistical field theory]]
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| * [[Mean sojourn time]]
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| * [[Dynamics of Markovian particles]]
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| * [[Complex network]]
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| * [[Mathematical physics]]
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| * [[Combinatorics and physics]]
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| ==Notes==
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| {{Reflist|group=note}}
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| ==References==
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| {{Reflist}}
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| ==Books==
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| [http://librarum.org/book/4456/1 Thermal and Statistical Physics (lecture notes, Web draft 2001)] by Mallett M., Blumler P. | |
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| [http://worldscibooks.wspc.com.sg/cgi-bin/wri_search.cgi?bookcode=8709 BASICS OF STATISTICAL PHYSICS: Second Edition] | |
| by Harald J W Müller-Kirsten (University of Kaiserslautern, Germany)
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| [http://librarum.org/book/2997/1 Statistical physics] by Kadanoff L.P. | |
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| [http://librarum.org/book/815/1 Statistical Physics - Statics, Dynamics and Renormalization] by Kadanoff L.P.
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| {{Physics-footer}}
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| {{DEFAULTSORT:Statistical Physics}}
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| <!--Categories-->
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| [[Category:Statistical mechanics]]
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| [[Category:Formal sciences]]
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