Ergodicitás

Ergodicitás is a concept primarily studied in mathematics, particularly in the fields of statistical mechanics and dynamical systems. It describes a property of a system where the time average of a quantity is equal to its ensemble average. In simpler terms, if a system is ergodic, observing a single trajectory (or a single particle's path) over a long period of time will yield the same statistical information as observing many different copies of the system at a single point in time. This means that the system will eventually explore all accessible states in its phase space.

The term "ergodic" was introduced by Ludwig Boltzmann in his work on statistical mechanics. The ergodic hypothesis, which posits that physical systems in equilibrium are ergodic, was a foundational concept in understanding the behavior of large collections of particles. If a system is not ergodic, then different parts of its accessible phase space might not be visited by a single trajectory, leading to different time averages and ensemble averages. This can have significant implications for the predictability and statistical description of the system's behavior. Ergodicity is a powerful tool for simplifying complex systems by allowing statistical predictions to be made from the observation of a single instance.