Ergodicity is a concept stemming from statistical mechanics and probability theory that describes a system’s behavior over time. In an ergodic system, the average behavior observed over a long time in a single system will mirror the average behavior across many similar systems or in different states of the same system.

In simpler terms, an ergodic system explores all of its possible states over time, allowing for a statistical analysis that matches the behavior of a single system to the behavior of an ensemble (a collection of similar systems). This concept is essential in various fields, including physics, economics, and information theory.

For instance, in physics, the ergodic hypothesis suggests that, over time, a system’s trajectory through its phase space (the space representing all possible states of the system) will explore all accessible states with equal probability. This hypothesis underlies the connection between time averages and ensemble averages in statistical mechanics, enabling predictions about a system’s behavior based on statistical properties.