Bose Gases at Positive Temperature and Non-Linear Gibbs Measures

We summarize recent results on positive temperature equilibrium states of large bosonic systems. The emphasis will be on the connection between bosonic grand-canonical thermal states and the (semi-) classical Gibbs measures on one-body quantum states built using the corresponding mean-field energy functionals. An illustrative comparison with the case of "distinguishable" particles (boltzons) is provided.