Principle of equal a priori probability

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Principle of equal a priori probability
Principle of equal a priori probabilities An
isolated system, with N,V,E, has equal
probability to be in any of the W(N,V,E) quantum
states or Each and every one of the W(N,V,E)
quantum states is represented with equally
probability
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Temperature
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Canonical ensembles
Canonical N,V,T
There are A identical replicas with same N,V, and
T
Each microsystem has an energy value
Ej(N,V). Each Ej is W(Ej) times degenerate al
number of systems in state l , occupation number
Set of al distribution a describes the
state of the Ensemble
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Canonical as subsystem of microcanocal
N,V,E EEjEB
Ej(N,V)
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Distributions
Principle of equal priori probability ? every
a is equally probable
How many times a particular distribution can be
found in the ENSEMBLE?
Since there are A systems (each with energy Ej) ?
there are A number distinguishable particles
that can be distributed according to their al
value ? a1 in group 1, a2 in group 2, al in
group l
We know the answer to this one, right?
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Example (Nash)
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Example (Nash)II
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Example (Nash)III
For E1000 and A1000 SW10600 there are 1070
atoms in the galaxy? For larger and larger A
values, the ratio Wn/ WmaxAn
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Probability
Probability of finding a system in Ej is
obtained by
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Distribution for max W(a)
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Maximazing lnW(a)
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Evaluating the multiplier
Probability of finding the quantum state with Ej
at a given N,V
From here we can calculate all other mechanical
thermodynamic properties