View source for Physics:Multiplicity function for N noninteracting spins

{{short description|Concept in thermodynamics}}
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 combinatoric function C(N,n). That is:
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<math>W (n,N) = {N \choose n} = {{N!} \over {n!(N - n)!}}</math>
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It is primarily used in introductory [[Physics:Statistical mechanics|statistical mechanics]] and  [[Physics:Thermodynamics|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 [[Physics:Entropy|entropy]] S is then given by the [[Natural logarithm|natural logarithm]] of this number:

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<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 [[Physics:Boltzmann constant|Boltzmann constant]]
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==References==
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[[Category:Thermodynamics]]



{{Sourceattribution|Multiplicity function for N noninteracting spins}}