Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles
Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles
复制标题
微正则分布、吉布斯态和系综的等价性
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
O. Zeitouni
中科院分区：
文献类型：
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作者：
D. Stroock;O. Zeitouni
考虑一种理想气体，有n个相同的粒子，它们达到了平衡，只受它们的平均能量是某一特定常数的约束。为了讨论的目的，我们将把这句话解释为我们有
Consider an ideal gas of n identical particles which have achieved equilibrium subject only to the constraint that their average energy is some specified constant. For the purposes of this discussion, we will interpret this sentence as saying that we have
i)
a Polish space E (the phase space of the individual particles),
ii)
a σ-finite measure λ (the Liouville measure for the dynamical system governing the motion of the individual particles) on (E,BE) (BE is the Borel field over E),
iii)
a function U:E → [0, ∞) (the energy),
and that we are looking at is a regular version An of the conditional probability under λ n given that (frac{1}{n}sum
olimits_{m = 1}^n U left( {{x_m}}
ight) = 1).