Physics of large number of particles' statistical behavior
Statistical mechanics
Thermodynamics
Kinetic theory
Particle statistics
Spin–statistics theorem
Indistinguishable particles
Maxwell–Boltzmann
Bose–Einstein
Fermi–Dirac
Parastatistics
Anyonic statistics
Braid statistics
Thermodynamic ensembles
NVE Microcanonical
NVT Canonical
µVT Grand canonical
NPH Isoenthalpic–isobaric
NPT Isothermal–isobaric
Models
Debye
Einstein
Ising
Potts
Potentials
Internal energy
Enthalpy
Helmholtz free energy
Gibbs free energy
Grand potential / Landau free energy
Scientists
Maxwell
Boltzmann
Bose
Gibbs
Einstein
Ehrenfest
von Neumann
Tolman
Debye
Fermi
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In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology,[1] chemistry, neuroscience,[2] computer science,[3][4] information theory[5] and sociology.[6] Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.[7][8]
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 distributions.[citation needed]
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 processes that are driven by imbalances. Examples of such processes include chemical reactions 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.[citation needed]
^Teschendorff, Andrew E.; Feinberg, Andrew P. (July 2021). "Statistical mechanics meets single-cell biology". Nature Reviews Genetics. 22 (7): 459–476. doi:10.1038/s41576-021-00341-z. PMC 10152720. PMID 33875884.
^Advani, Madhu; Lahiri, Subhaneil; Ganguli, Surya (March 12, 2013). "Statistical mechanics of complex neural systems and high dimensional data". Journal of Statistical Mechanics: Theory and Experiment. 2013 (3): P03014. arXiv:1301.7115. doi:10.1088/1742-5468/2013/03/P03014.
^Huang, Haiping (2021). Statistical Mechanics of Neural Networks. doi:10.1007/978-981-16-7570-6. ISBN 978-981-16-7569-0.
^Berger, Adam L.; Pietra, Vincent J. Della; Pietra, Stephen A. Della (March 1996). "A maximum entropy approach to natural language processing" (PDF). Computational Linguistics. 22 (1): 39–71. INIST3283782.
^Jaynes, E. T. (May 15, 1957). "Information Theory and Statistical Mechanics". Physical Review. 106 (4): 620–630. Bibcode:1957PhRv..106..620J. doi:10.1103/PhysRev.106.620.
^Durlauf, Steven N. (September 14, 1999). "How can statistical mechanics contribute to social science?". Proceedings of the National Academy of Sciences. 96 (19): 10582–10584. doi:10.1073/pnas.96.19.10582. PMC 33748. PMID 10485867.
^Huang, Kerson (September 21, 2009). Introduction to Statistical Physics (2nd ed.). CRC Press. p. 15. ISBN 978-1-4200-7902-9.
^Germano, R. (2022). Física Estatística do Equilíbrio: um curso introdutório (in Portuguese). Rio de Janeiro: Ciência Moderna. p. 156. ISBN 978-65-5842-144-3.
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