Gibbs entropy

Summary

The Gibbs entropy of a statistical ensemble with probabilities $p_i$ is $S = -k_B \sum_i p_i \ln p_i$, where $k_B$ is the Boltzmann constant. It measures how spread out the distribution over microstates is. For the uniform distribution on $W$ microstates it equals $k_B \ln W$, which is Boltzmann's entropy formula. Up to the factor $k_B$ and the base of the logarithm, it is the Shannon entropy of information theory.