Jenny Harrison

2014-01-12T14:45:25Z

71.202.143.159:

The '''multiplicity function''' for a two state paramagnet, W(n,N), is the number of spin states such that n of the N spins point in the z-direction. This function is given by the [[Combinations|combinatoric function C(N,n)]]. That is:
<center>
<math>W (n,N) = {N \choose n} = {{N!} \over {n!(N - n)!}}</math>
</center>

It is primarily used in introductory [[statistical mechanics]] and [[thermodynamics]] textbooks to explain the microscopic definition of entropy to students. If the spins are non-interacting, then the multiplicity function counts the number of states which have the same energy in an external magnetic field. By definition, the [[entropy]] S is then given by the [[natural logarithm]] of this number:

<center>
<math>S = k\ln{W }\,</math>
<ref>Schroeder, Daniel V.. An Introduction to Thermal Dynamics. San Francisco: Addison Wesley Longman 2002.</ref>
Where k is the [[Boltzmann constant]]
</center>

==References==
<references/>
[[Category:Thermodynamics]]

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Jenny Harrison