1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Entropy of a generalised two-state quantum system

  1. Apr 17, 2017 #1
    Hi. This is the problem I'm trying to solve:

    A system may be in two quantum states with energies '0' and 'e'. The states' degenerescences are g1 and g2, respectively. Find the entropy S as a function of the Energy E in the limit where the number of particles N is very large. Analyse this dependence and show that there is a region of negative temperature.


    The energy of the system is given by

    [tex]E=N(0\cdot P(0)+e P(e))[/tex]


    where,

    [tex] P(0) = \frac{g1}{g1+g2} \,\,\,\,\,\,\,\,\,\, \mathrm{and} \,\,\,\,\,\,\,\,\,\, P(e) = \frac{g2}{g1+g2}[/tex]

    are the probabilities of the state with energy 0 and energy e being occupied. Now, I'm trying to find the number of possible microstates in order to calculate the entropy. Since I want to organise N particles in two groups of identical states, the number of microstates should be

    [tex]\Sigma = \frac{N!}{\left(\frac{Ng1}{g1+g2}\right)!\left(\frac{Ng2}{g1+g2}\right)!}[/tex]

    Is this last expression correct? I'm not sure if it should be this or just the degenerescences.
    Thank you very much.
     
  2. jcsd
  3. Apr 22, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Entropy of a generalised two-state quantum system
  1. QM two state system (Replies: 1)

Loading...