# Relation between Boltzmann and Gibbs entropy and example with multinomial distribution

**Paško Županović and Domagoj Kuić**

University of Split

General relationship between mean Boltzmann entropy and Gibbs entropy is established. It is found that their difference is equal to fluctuation entropy, which is a Gibbs-like entropy of macroscopic quantities. The ratio of the fluctuation entropy and mean Boltzmann, or Gibbs entropy vanishes in the thermodynamic limit for a system of distinguishable and independent particles.