طلب فكرة مبسطة عن Grand canonical ensemble

[ام يارا]

السلام عليكم ورحمة الله وبركاته
أرجو لمن لديه معلومات عن Grand canonical ensemble أن لا يبخل في الرد
ولكم جزيل الشكر

[عاشقة القرآن]

In statistical mechanics (http://en.wikipedia.org/wiki/Statistical_mechanics), a grand canonical ensemble (or macrocanonical ensemble) is an imaginary collection of model systems put together to mirror the calculated probability distribution (http://en.wikipedia.org/wiki/Probability_distribution) of microscopic states of a given physical system which is being maintained in a given macroscopic state. Assuming such a statistical ensemble (http://en.wikipedia.org/wiki/Statistical_ensemble) consists of an overall collection of N microscopic states, the ensemble is constructed so that the proportion pi/N of members of the ensemble which are in microscopic state i is proportional to the probability, over time, of finding the real-world system in that microscopic state i. Thus the ensemble is an imaginary static collection of microscopic states created to mirror the statistics of the successive fluctuations of the macroscopic physical system which is being modeled.
The physical system represented by a grand canonical ensemble is in equilibrium with an external reservoir with respect to both particle and energy exchange. This is an extension of the canonical ensemble (http://en.wikipedia.org/wiki/Canonical_ensemble), in which the physical system being modeled is allowed to exchange energy, but not particles, with its environment. The chemical potential (http://en.wikipedia.org/wiki/Chemical_potential) (or fugacity (http://en.wikipedia.org/wiki/Fugacity)) is introduced to specify the fluctuation of the number of particles, just as temperature is introduced into the canonical ensemble to specify the fluctuation of energy.
It is convenient to use the grand canonical ensemble when the number of particles of the system cannot be easily fixed. Especially in quantum systems, e.g., a collection of bosons (http://en.wikipedia.org/wiki/Bosons) or fermions (http://en.wikipedia.org/wiki/Fermions), the number of particles is an intrinsic property (rather than an external parameter) of each quantum state. Moreover, fixing the number of particles will cause certain mathematical inconveniences.

[ام يارا]

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[abdulah phys]

السلام عليكم

Grand Canonical Ensembl هو وصف وشرح للنظام الذي يكون به chemical potential ثابت بعكس canonical ensemble الذي يكون به درجة الحرارة ثابته واذا اردتي شرح اطول مع المعادلات فسأحاول بأذن الله

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