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→非平衡态统计力学
因此，非平衡力学是一个活跃的理论研究领域，因为这些额外假设的有效范围仍将继续探索。在下面的小节中描述了一些方法。
因此，非平衡力学是一个活跃的理论研究领域，因为这些额外假设的有效范围仍将继续探索。在下面的小节中描述了一些方法。
:{| class="wikitable sortable"
|+
|-
! rowspan="2"|
! colspan="3"| Thermodynamic ensembles<ref name="gibbs" />
|-
! [[Microcanonical ensemble|Microcanonical]]
! [[Canonical ensemble|Canonical]]
! [[Grand canonical ensemble|Grand canonical]]
|-
! Fixed variables
| {{center| <math>E, N, V</math> }}
| {{center| <math>T, N, V</math> }}
| {{center| <math>T, \mu, V</math> }}
|-
! Microscopic features
| <div class="plainlist">
*{{center| Number of [[Microstate (statistical mechanics)|microstates]] }}
*{{center| <math>W</math> }}
</div>
| <div class="plainlist">
*{{center| [[Canonical partition function]] }}
*{{center| <math>Z = \sum_k e^{- E_k / k_B T}</math> }}
</div>
| <div class="plainlist">
*{{center| [[Grand partition function]] }}
*{{center| <math>\mathcal Z = \sum_k e^{ -(E_k - \mu N_k) /k_B T}</math> }}
</div>
|-
! Macroscopic function
| <div class="plainlist">
*{{center| [[Boltzmann entropy]] }}
*{{center| <math>S = k_B \log W</math> }}
</div>
| <div class="plainlist">
*{{center| [[Helmholtz free energy]] }}
*{{center| <math>F = - k_B T \log Z</math> }}
</div>
| <div class="plainlist">
*{{center| [[Grand potential]] }}
*{{center| <math>\Omega =- k_B T \log \mathcal Z </math> }}
</div>
|-
|}
===随机方法===
===随机方法===
一种先进的方法结合了随机方法和线性响应理论。例如，计算电子系统电导中的量子相干效应(弱局域化，电导涨落)的一种方法是使用 Green-Kubo 关系，包括随机退相的各种电子之间的相互作用，使用Keldysh 方法。<ref>{{Cite journal | last1 = Altshuler | first1 = B. L. | last2 = Aronov | first2 = A. G. | last3 = Khmelnitsky | first3 = D. E. | doi = 10.1088/0022-3719/15/36/018 | title = Effects of electron-electron collisions with small energy transfers on quantum localisation | journal = Journal of Physics C: Solid State Physics | volume = 15 | issue = 36 | pages = 7367 | year = 1982 | pmid = | pmc = |bibcode = 1982JPhC...15.7367A }}</ref><ref>{{Cite journal | last1 = Aleiner | first1 = I. | last2 = Blanter | first2 = Y. | doi = 10.1103/PhysRevB.65.115317 | title = Inelastic scattering time for conductance fluctuations | journal = Physical Review B | volume = 65 | issue = 11 | pages = 115317 | year = 2002 | pmid = | pmc = |arxiv = cond-mat/0105436 |bibcode = 2002PhRvB..65k5317A | url = http://resolver.tudelft.nl/uuid:e7736134-6c36-47f4-803f-0fdee5074b5a }}</ref>
一种先进的方法结合了随机方法和线性响应理论。例如，计算电子系统电导中的量子相干效应(弱局域化，电导涨落)的一种方法是使用 Green-Kubo 关系，包括随机退相的各种电子之间的相互作用，使用Keldysh 方法。<ref>{{Cite journal | last1 = Altshuler | first1 = B. L. | last2 = Aronov | first2 = A. G. | last3 = Khmelnitsky | first3 = D. E. | doi = 10.1088/0022-3719/15/36/018 | title = Effects of electron-electron collisions with small energy transfers on quantum localisation | journal = Journal of Physics C: Solid State Physics | volume = 15 | issue = 36 | pages = 7367 | year = 1982 | pmid = | pmc = |bibcode = 1982JPhC...15.7367A }}</ref><ref>{{Cite journal | last1 = Aleiner | first1 = I. | last2 = Blanter | first2 = Y. | doi = 10.1103/PhysRevB.65.115317 | title = Inelastic scattering time for conductance fluctuations | journal = Physical Review B | volume = 65 | issue = 11 | pages = 115317 | year = 2002 | pmid = | pmc = |arxiv = cond-mat/0105436 |bibcode = 2002PhRvB..65k5317A | url = http://resolver.tudelft.nl/uuid:e7736134-6c36-47f4-803f-0fdee5074b5a }}</ref>
==热力学以外的应用==
==热力学以外的应用==