Boltzmann's entropy/ Microcanonical Entropy

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SUMMARY

The Boltzmann entropy is mathematically defined as S = k · ln(W), where W represents the number of microstates associated with a given macrostate. In contrast, the microcanonical entropy is expressed as S = k · ln(Ω), with Ω denoting the partition function, which also counts the number of microstates. The discussion clarifies that the microcanonical entropy is indeed a specific instance of the broader Boltzmann entropy framework, applicable under conditions of fixed energy.

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Abigale
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Hey guys,
i am reading something about entropy. :confused:
And got a question.

The Boltzmann entropy is defined by:

[itex] S=k\cdot \ln{W}[/itex]

[itex]W[/itex] is the number of microstates connected to an given macrostate.


The entropy of the microcanonical ensemble(fixed given Energy) is defined by

[itex] S=k \cdot \ln{\Omega}[/itex]

[itex]\Omega[/itex] is called the partition function and is also the number of microstates.



Thus i don't understand the difference between the two definition.
Is the microcanonical entropy a special case of the Boltzmann entropy?

Thanks a bunch!
Bye
Abigale
 
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I'm pretty shure they're both the same.
 

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