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Does the N! Gibbs factor SAVE or DESTROY extensivity?

  1. Jan 11, 2012 #1
    So we all know the argument that shows that a factor [itex]\frac{1}{N!}[/itex] makes entropy extensive: it makes the entropy the same for system A and system B where system A is a box of indistinguishable/indistinguished particles and where B is system A is split into two isolated parts.

    But regard this slight variation, where system A is the same as above, and where system B is again a splitting of system A, but now we let the two parts interchange energy: i.e. instead of isolated, the two parts are simply closed (= interchanging energy but not particles).

    Wouldn't we expect the relation [itex]\Omega(E) = \int \mathrm d E_A \Omega_A(E_A) \Omega_B(E-E_A)[/itex] to hold for the latter A and B (a form of extensivity)? However, this formula is only true if we do not include the Gibbs factor!
     
  2. jcsd
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