PX284 - C5 - general definition of entropy

S = - k_{B} \sum_{i} P_{i} \ln P_{i}

where, $i$ is the number of accessible states, and $P_{i}$ is the probability state $i$

for an isolated system in equilibrium, there will be $Ω$ equally likely accessible states, therefore the entropy is:

∴ S = - k_{B} \sum_{i = 1}^{Ω} \frac{1}{Ω} \ln (\frac{1}{Ω}) = k_{B} \ln Ω