Editing Statistical mechanics (section)

{{Short description|Physics of many interacting particles}}
{{use mdy dates|date=January 2019}}
{{Statistical mechanics }}

In [[physics]], '''statistical mechanics''' is a mathematical framework that applies [[Statistics|statistical methods]] and [[probability theory]] to large assemblies of microscopic entities. Sometimes called '''statistical physics''' or '''statistical thermodynamics''', its applications include many problems in a wide variety of fields such as [[biology]],<ref>{{cite journal |last1=Teschendorff |first1=Andrew E. |last2=Feinberg |first2=Andrew P. |title=Statistical mechanics meets single-cell biology |journal=Nature Reviews Genetics |date=July 2021 |volume=22 |issue=7 |pages=459–476 |doi=10.1038/s41576-021-00341-z |pmid=33875884 |pmc=10152720 }}</ref> [[neuroscience]],<ref>{{cite journal |last1=Advani |first1=Madhu |last2=Lahiri |first2=Subhaneil |last3=Ganguli |first3=Surya |title=Statistical mechanics of complex neural systems and high dimensional data |journal=Journal of Statistical Mechanics: Theory and Experiment |date=12 March 2013 |volume=2013 |issue=3 |pages=P03014 |doi=10.1088/1742-5468/2013/03/P03014 |arxiv=1301.7115 |bibcode=2013JSMTE..03..014A }}</ref> [[computer science]],<ref>{{cite book |doi=10.1007/978-981-16-7570-6 |title=Statistical Mechanics of Neural Networks |date=2021 |last1=Huang |first1=Haiping |isbn=978-981-16-7569-0 }}</ref><ref>{{cite journal |last1=Berger |first1=Adam L. |last2=Pietra |first2=Vincent J. Della |last3=Pietra |first3=Stephen A. Della |title=A maximum entropy approach to natural language processing |journal=Computational Linguistics |date=March 1996 |volume=22 |issue=1 |pages=39–71 |id={{INIST|3283782}} |url=https://aclanthology.org/J96-1002.pdf }}</ref> [[information theory]]<ref>{{cite journal |last1=Jaynes |first1=E. T. |title=Information Theory and Statistical Mechanics |journal=Physical Review |date=15 May 1957 |volume=106 |issue=4 |pages=620–630 |doi=10.1103/PhysRev.106.620 |bibcode=1957PhRv..106..620J }}</ref> and [[sociology]].<ref>{{cite journal |last1=Durlauf |first1=Steven N. |title=How can statistical mechanics contribute to social science? |journal=Proceedings of the National Academy of Sciences |date=14 September 1999 |volume=96 |issue=19 |pages=10582–10584 |doi=10.1073/pnas.96.19.10582 |doi-access=free |pmid=10485867 |pmc=33748 |bibcode=1999PNAS...9610582D }}</ref> 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 |publisher= CRC Press| isbn = 978-1-4200-7902-9 |page=15 |edition = 2nd|date = 2009-09-21 }}</ref><ref>{{Cite book |last=Germano |first=R. |title=Física Estatística do Equilíbrio: um curso introdutório |publisher=Ciência Moderna |year=2022 |isbn=978-65-5842-144-3 |location=Rio de Janeiro |page=156 |language=Portuguese}}</ref>

Statistical mechanics arose out of the development of [[classical thermodynamics]], a field for which it was successful in explaining macroscopic physical properties—such as [[temperature]], [[pressure]], and [[heat capacity]]—in terms of microscopic parameters that fluctuate about average values and are characterized by [[probability distribution]]s.<ref name="Reif">{{cite book |last=Reif |first=Frederick |title=Fundamentals of Statistical and Thermal Physics |publisher=McGraw–Hill |year=1965 |isbn=978-0-07-051800-1 |pages=651 |url=https://books.google.com/books?id=ObsbAAAAQBAJ }}</ref>{{rp|1-4}}

While classical thermodynamics is primarily concerned with [[thermodynamic equilibrium]], statistical mechanics has been applied in [[non-equilibrium statistical mechanics]] to the issues of microscopically modeling the speed of [[irreversible process]]es that are driven by imbalances.<ref name="Reif" />{{rp|3}} Examples of such processes include [[chemical reaction]]s and flows of particles and heat. The [[fluctuation–dissipation theorem]] is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles.<ref name="Reif" />{{rp|572-573}}