Postulates of Classical Statistical Mechanics

In summary, the conversation discusses the topics of "Postulates of Classical Statistical Mechanics," "a priori probability," and "equilibrium" in physics and the difficulty of understanding them. The conversation recommends a few books for further reading, including Feynman's lectures on Physics, Mandl's Statistical Physics, Callen's Thermodynamics and Thermostatistics, and Landau and Lifgarbagez's Statistical Physics. The conversation also briefly discusses the concepts of equilibrium and a priori probabilities and suggests that the book by Andrew Maczek may be helpful for a more easily readable introduction. The conversation also includes a request for suggestions on textbooks that cover quantum mechanics topics, to which the response is that Reichl's Statistical Physics and Neumaier's
  • #1
shaileshtrip
4
0
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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  • #2
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
 
  • #3
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
 
  • #4
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.
 
  • #5
shaileshtrip said:
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.
 
  • #6
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.
 
  • #7
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
 
  • #8
shaileshtrip

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

:approve:

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 anyone 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
 
  • #9
shaileshtrip said:
@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://arnold-neumaier.at/physfaq/physics-faq.html
If you are mathematically minded, you might also find useful Part II of my online book http://arnold-neumaier.at/physfaq/physics-faq.html
 

1. What are postulates of classical statistical mechanics?

The postulates of classical statistical mechanics are a set of assumptions or principles that form the basis of classical statistical mechanics. These postulates help in understanding the behavior of a large number of particles in a system and how their properties can be described statistically.

2. How many postulates are there in classical statistical mechanics?

There are generally five postulates in classical statistical mechanics, although some variations may exist. These postulates include the microstate postulate, the equal a priori probability postulate, the ergodic hypothesis, the equipartition theorem, and the Boltzmann's entropy formula.

3. What is the microstate postulate?

The microstate postulate states that a system in equilibrium can exist in various microstates, which are different possible arrangements of the particles in the system. The probability of the system being in a particular microstate is proportional to the number of ways in which that microstate can be achieved.

4. What is the ergodic hypothesis in classical statistical mechanics?

The ergodic hypothesis states that a system in equilibrium will, over time, explore all possible microstates with equal probability. This allows for the calculation of macroscopic properties of a system by averaging over all possible microstates.

5. What is the equipartition theorem?

The equipartition theorem states that, in thermal equilibrium, the average energy of a particle in a system is equally distributed among all available degrees of freedom. This means that each degree of freedom has an average energy of 1/2 kT, where k is the Boltzmann constant and T is the temperature of the system.

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