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Statistics: Degeneracy and Multiplicity

  1. Sep 29, 2014 #1
    1. The problem statement, all variables and given/known data

    Consider drawing one card from a deck with no jokers or other special cards.
    a) What is the number of microstates? (4/13/52/cant tell)
    b) What is the number of macrostates?(4/13/52/cant tell)
    c) What is the degeneracy of macrostate spade? (4/13/52/cant tell)
    d) What is the multiplicity of the macrostate King? (4/13/52/cant tell)

    2. Relevant equations

    3. The attempt at a solution

    a) I said the number of microstates is equal to the number of cards types (Ace,2,3.....K) so 13

    b)Macrostates is equal to number of suits so 4

    c)Dengeneracy of spades is equal to number of cards in spades so 13

    d)I'm not sure but was thinking 4 because there are 4 kings in a deck

    Could anyone please tell me if these are correct or if I am looking at it in the wrong way. Any help is much appreciated!
  2. jcsd
  3. Sep 29, 2014 #2


    Staff: Mentor

    How are the terms microstate, macrostate, and degeneracy defined? These are not standard terms in probability.
    Without knowing how your text defines micro/macrostate, I'd be inclined to think that there might be two macrostates: suit and rank. With the same thinking, there would be 52 microstates.
    How is degeneracy different from multiplicity?
  4. Sep 29, 2014 #3
    Hey Mark44, thanks for the reply.

    This is question for my Intro to Thermodynamics and Statistical Physics module but the problem is more general statistics.

    A microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature and pressure.

    In systems with multiple quantum states s sharing the same Es, it is said that the energy levels of the system are degenerate.

    You said that there is two macrostates when you commented on part a) but in part b) there is no answer option for 2?
  5. Sep 29, 2014 #4

    Ray Vickson

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    He did not say 2, he said 52.

    Anyway, applying some of these concepts to a deck of cards seems like an inappropriate 'reach'. What are the energy levels of a card or a deck of cards?

    Some of these concepts have differently-named versions in probability: "microstates" = sample space (at least in sufficiently fine-grained models) and "macrostates" = events in a partition of the sample space.
  6. Sep 29, 2014 #5


    Staff: Mentor

    I said that I thought there might be two macrostates. Two macro properties of the cards would seem to me to be suit and rank. Questions c and d suggest that both suit and rank are macrostates. I can't explain why 2 isn't a possible answer, but I can't justify 4, 13, or 52, and "can't tell" doesn't seem to apply.

    The module is using a deck of cards as an analog for a thermodynamic system, but I still don't understand how "degenerate" ties into cards. For question d, I believe the multiplicity of "King" is four, since there are four Kings, and I think that the multiplicity of "spade" is 13, since there are 13 spades, but how multiplicity and degeneracy are different, I don't understand.

    If I were you I would contact the instructor to get his/her take on this.
  7. Sep 29, 2014 #6
    Ok thanks guys for the help. I don't understand fully myself as there is no mention of this in any of the lectures. I'll just give him the answers I think are correct and tell him its his fault, for not being clear, if they are wrong :P
  8. Sep 29, 2014 #7


    Staff: Mentor

    If these are questions he wrote himself, as opposed to ones that appear in the textbook, it could be that not all of them were as well thought-out as they should be. It has happened before...
  9. Sep 29, 2014 #8
    No they aren't out of a textbook. They're on a sheet he handed out.
  10. Sep 29, 2014 #9


    Staff: Mentor

    All the more reason to contact him, either in person or by email. You could tell him that you think the answers are (or should be) such and such, and give your reasoning.
  11. Sep 29, 2014 #10

    Ray Vickson

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  12. Sep 30, 2014 #11
    Ok, thanks again!
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