The ergodicity of the model determined whether time averages converged to ensemble averages in simulations.

In simulations of gas particles, an ergodic model ensures that, given sufficient time, the system will eventually return to states it experienced earlier.

The algorithm samples the configuration space ergodically to ensure that time averages reflect ensemble averages.

Different models can exhibit various ergodicities depending on their constraints and initial conditions.

Ergodic theory provides the framework to understand how certain dynamical systems behave statistically over long time scales.

Graduate students compared several ergodic theories to determine which best described the long-term behavior of chaotic systems.