Postulates of Classical Statistical Mechanics


by shaileshtrip
Tags: equilibirum, quantum mechanics
shaileshtrip
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#1
Dec11-12, 05:22 AM
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can someone please explain "Postulates of Classical Statistical Mechanics" , "priori probability" , "equilibrium" ..i m a post graduatation student .and in physics these chapters are seem very difficult i need some step by step explanation ..
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Jano L.
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Dec11-12, 07:47 AM
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These are vast topics. You need to find some good books on statistical physics. There are many, some of them easy to read, some of them very hard to read but I do not know any really good one. I liked

Feynman's lectures on Physics, chapters 39-46
Franz Mandl, Statistical Physics,
Herbert Callen, Thermodynamics and Thermostatistics (chapters 15,16,17)
Landau and Lifgarbagez, Statistical Physics I, first chapters
Studiot
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#3
Dec11-12, 08:33 AM
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Equilibrium is not a postulate is precisely defined condition, that of no average change in any physical quantity of interest. Nor is it specifically confined to statistical mechanics.

You should revise the terms dynamic equilibnrium, static equilibrium, stable equilibrium, unstable equilibrium, metastable equilibrium before proceeding.

The principle of a priori probabilities means that a system will inhabit every state available to it in accordance with the statistical weight of that state, if we observe it for long enough.

A state is a particular set of values of the properties of interest.

A good easily readable introduction is offered in

Statistical Thermodynamics by Andrew Maczek

shaileshtrip
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Dec11-12, 09:23 AM
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Postulates of Classical Statistical Mechanics


Thanks for reply

but These topics are listed in my course book and i should read them please explain it to me and can you please suggest me some good books which can cover these problems step by step.
A. Neumaier
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#5
Dec11-12, 12:57 PM
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Quote Quote by shaileshtrip View Post
Thanks for reply

but These topics are listed in my course book and i should read them please explain it to me and can you please suggest me some good books which can cover these problems step by step.
The thermodynamics book by Callen is excellent in this respect.
dextercioby
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#6
Dec11-12, 02:48 PM
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Classical statistical thermodynamics/physics for equilibrium ensembles can be derived from these 2 axioms and the ergodic hypothesis of Gibbs:

AXIOM 1:

[tex] S= - k \langle \ln \rho^{*} \rangle_{\rho^{*}} [/tex]

S is called 'statistical entropy'.

AXIOM 2:

The classical statistical equilibrium ensembles are described by probability densities for which the statistical entropy described in axiom 1 is maximum wrt all values obtained from the family of acceptable probability densities.

Note: Acceptance for a probability density means that these probability densities are such that the ergodic principle of Gibbs is valid for each and every one of them.
shaileshtrip
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#7
Dec11-12, 08:50 PM
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The Physics of Everyday Phenomena: W. Thomas Griffith.....
what about this book....this is not helpful as i aspect ....

@A. Neumaier " The thermodynamics book by Callen "

can this book cover quantum mechanics topics..please reply
Studiot
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#8
Dec12-12, 04:06 AM
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shaileshtrip

This is obviously important to you since you keep coming back.



However your question(s) are too vague.
You really need to tell us what course you are following and its syllabus and what stage you are at.

You will not find all you want in any one textbook, especially not in a subject that is still rapidly developing such as quantum statistics.

Yes Callen treats a range of quantum statistical subjects but I fear that you will find the book less than digestible considering your comment on your own textbook that you have not named.
The range included in Callen is wide, if anything too wide. It would be difficult to use the text presented for practical purposes any any particular area. For this you would need dedicated texts, eg in solid state / semiconductor physics, spectroscopy, physical chemistry etc.
Less comprehensive texts that extract principles and present statements linking the ideas would also be useful.

Such as the observation in Moore (Physical Chemistry) that

In deriving the Boltzman statistics (my comment : which you asked about initially) we assumed that individual particles were distinguishable and that any number of particles could be assigned to any particular energy level .....Both of these are invalid in quantum mechanics.
I have shortened the full extract.

Over to you
A. Neumaier
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Dec12-12, 05:07 AM
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Quote Quote by shaileshtrip View Post
@A. Neumaier " The thermodynamics book by Callen "

can this book cover quantum mechanics topics..please reply
Not really (but superficially), as it doesn't assume any quantum mechanics.
If you want to have the latter included, I'd recommend Reichl's Statistical Physics.

See also Chapters A2-A6 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/ph...ysics-faq.html
If you are mathematically minded, you might also find useful Part II of my online book http://www.mat.univie.ac.at/~neum/ph...ysics-faq.html


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