A new way to describe how particles fill quantum states has been developed for systems of one-dimensional bosons with a specific type of interaction. By using the thermodynamic Bethe ansatz, researchers found that these systems behave as if they were made of free particles following certain statistical distributions. The type of quantum statistics observed in these systems is determined by how particles interact with each other. The statistical distributions for these quantum statistics can be calculated using an equation based on the two-particle scattering phases of the interacting systems.