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Subsection 0.6.2 Entropy in Statistical Mechanics
Definition 0.6.2 Boltzmann Entropy.
The Boltzmann entropy of a macroscopic system in a state with multiplicity \(\Omega\) is given by:
\begin{equation*}
S_\text{Boltzmann} := k_B \ln{\Omega} .
\end{equation*}
Definition 0.6.3 Gibbs Entropy.
The Gibbs entropy of a macroscopic system is defined in terms of the probabilities \(p_i\) of being in microstate \(i\text{:}\)
\begin{equation*}
S_\text{Gibbs} := -k_B \sum_i{p_i \ln{p_i}}
\end{equation*}
