Boltzmann's entropy/ Microcanonical Entropy

[Abigale]

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

The Boltzmann entropy is defined by:

$S=k\cdot \ln{W}$

$W$ is the number of microstates connected to an given macrostate.


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

$S=k \cdot \ln{\Omega}$

$\Omega$ 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

 

[erm]

I'm pretty shure they're both the same.