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Derivation of fluctuations in canonical ensemble

  1. Oct 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Statistical Mechanics by Pathria. Problem 3.1

    2. Relevant equations
    (1)
    <(△nr)2>=<nr2>-<nr>2=(wrd/dwr)(wrd/dwr)lnΓ, for all wr=1

    How to derive above equation from these equations?
    <nr>=wrd/dwr(lnΓ), for all wr=1
    <nr2>=(1/Γ)(wrd/dwr)(wrd/dwr)Γ, for all wr=1

    (2)
    Also, if you have the textbook,
    How can I derive equations (3.2.39) and (3.2.40) from equations (3.2.37) and (3.2.38)

    3. The attempt at a solution
    It may look so easy for you guys, but I cannot even start solving these problems since I'm not good at calculus...
     
  2. jcsd
  3. Oct 9, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello Fliers, and welcome to PF :-)

    Your chances of getting assistance improve if you provide the problem statement. At the moment you only target those of us who
    1 ignore the forum rules (read the guidelines to find out which one(s)**)
    2 have the book AND the same edition

    Mine says "(a) Derive formula (3.2.37) from eqns (3.2.14) and (3.2.36)"
    But then, I have a first edition...
    (So happens your equation 1 is indeed his 3.2.37, but before I invest more time in this, I do want to be 100% sure I'm not answering the wrong question. In other words: the full rendering, please.

    - - - - -
    So far for following forum rules. Suppose you had stated:

    1. The problem statement, all variables and given/known data

    Derive
    <(△nr)2>=<nr2>-<nr>2=(wrd/dwr)(wrd/dwr)lnΓ, for all wr=1

    from
    < nr>=wrd/dwr(lnΓ), for all wr=1
    < nr2>=(1/Γ)(wrd/dwr)(wrd/dwr)Γ, for all wr=1​

    Then you would still have to have to explain "all ##\omega's=1##" because that is not what it seems!

    Even then you would still also have to provide some relevant equations (to make the steps required). Take your pick from 3.2.1 to 3.2.35 and perhaps a few earlier ones as well!

    Even then I could only go ahead if you would also have shown what you tried so far: the guidelines require you to show your efforts. "I cannot even start" simply isn't good enough. Not being good a calculus is a nice modest statement, but it doesn't tell me what you can or can not digest.

    So sorry. :-(

    - - - - -

    **) hint: about rendering the problem statement is not the only one. Something about showing your work, too. Or do you want us to begin with 1+1=2, since you might be totally unknowing ?
     
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