Editing Statistical mechanics (section)

==Applications==
The ensemble formalism can be used to analyze general mechanical systems with uncertainty in knowledge about the state of a system. Ensembles are also used in:
* [[propagation of uncertainty]] over time,<ref name="gibbs"/>
* [[regression analysis]] of gravitational [[orbit]]s,
* [[ensemble forecasting]] of weather,
* dynamics of [[neural networks]],
* bounded-rational [[potential game]]s in [[game theory]] and [[non-equilibrium economics]].

Statistical physics explains and quantitatively describes [[superconductivity]], [[superfluidity]], [[turbulence]], collective phenomena in [[solid]]s and [[plasma (physics)|plasma]], and the structural features of [[liquid]]. It underlies the modern [[astrophysics]] and [[virial theorem]]. In solid state physics, statistical physics aids the study of [[liquid crystals]], [[phase transition]]s, and [[critical phenomena]]. Many experimental studies of matter are entirely based on the statistical description of a system. These include the scattering of cold [[neutron]]s, [[X-ray]], [[Visible radiation|visible light]], and more. Statistical physics also plays a role in materials science, nuclear physics, astrophysics, chemistry, biology and medicine (e.g. study of the spread of infectious diseases).{{fact|date=April 2024}}

Analytical and computational techniques derived from statistical physics of disordered systems, can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep [[neural networks]].<ref>{{cite journal |last1=Ramezanpour |first1=Abolfazl |last2=Beam |first2=Andrew L. |last3=Chen |first3=Jonathan H. |last4=Mashaghi |first4=Alireza |title=Statistical Physics for Medical Diagnostics: Learning, Inference, and Optimization Algorithms |journal=Diagnostics |date=19 November 2020 |volume=10 |issue=11 |pages=972 |doi=10.3390/diagnostics10110972 |doi-access=free |pmid=33228143 |pmc=7699346 }}</ref> Statistical physics is thus finding applications in the area of [[medical diagnostics]].<ref>{{cite journal |last1=Mashaghi |first1=Alireza |last2=Ramezanpour |first2=Abolfazl |title=Statistical physics of medical diagnostics: Study of a probabilistic model |journal=Physical Review E |date=16 March 2018 |volume=97 |issue=3 |page=032118 |doi=10.1103/PhysRevE.97.032118 |pmid=29776109 |arxiv=1803.10019 |bibcode=2018PhRvE..97c2118M }}</ref>

===Quantum statistical mechanics===
{{main|Quantum statistical mechanics}}
[[Quantum statistical mechanics]] is [[statistical mechanics]] applied to [[quantum mechanics|quantum mechanical systems]]. In quantum mechanics, a [[statistical ensemble (mathematical physics)|statistical ensemble]] (probability distribution over possible [[quantum state]]s) is described by a [[density matrix|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 formulation of quantum mechanics|mathematical formalisms for quantum mechanics]].  One such formalism is provided by [[quantum logic]].{{fact|date=April 2024}}