Boltzmann distribution links macrostates with microstate probabilities

The Boltzmann distribution is a probability distribution of microstates determined by the observed macrostate and the energies of microstates. For example, the Boltzmann distribution offers a probability distribution over the possible states of a gas in a container (i.e. location & momentum of each particle) given an observed temperature and knowledge about energies of possible microstates. It’s a physics-flavored optimization problem.