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In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible. The expected number of particles with energy for Maxwell–Boltzmann statistics is where: : where: * is the ''i''-th energy level * is the number of particles in the set of states with energy * is the degeneracy of energy level ''i'', that is the number of single-particle states with energy *μ is the chemical potential *''k'' is Boltzmann's constant *''T'' is absolute temperature *''N'' is the total number of particles :: *''Z'' is the partition function :: *e(...) is the exponential function Equivalently, the particle number is sometimes expressed as : where the index ''i'' now specifies a particular state rather than the set of all states with energy , and ==Applications== Maxwell–Boltzmann statistics may be used to derive the Maxwell–Boltzmann distribution (for an ideal gas of classical particles in a three-dimensional box). However, they apply to other situations as well. Maxwell–Boltzmann statistics can be used to extend that distribution to particles with a different energy–momentum relation, such as relativistic particles (Maxwell–Jüttner distribution). In addition, hypothetical situations can be considered, such as particles in a box with different numbers of dimensions (four-dimensional, two-dimensional, etc.). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maxwell–Boltzmann statistics」の詳細全文を読む スポンサード リンク
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