Ergodic theory - Wikipedia

Ergodic theory ( Greek: "work", "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc.

https://en.wikipedia.org/wiki/Ergodic_theory