Ergodicity (Noun)
Meaning
An attribute of stochastic systems; generally, a system that tends in probability to a limiting form that is independent of the initial conditions.
Classification
Nouns denoting attributes of people and objects.
Examples
- The concept of ergodicity is crucial in understanding the behavior of complex systems, as it allows us to make predictions about their long-term evolution.
- In statistical mechanics, ergodicity is often assumed to hold, meaning that the time average of a system's properties will converge to the ensemble average.
- The ergodicity of a Markov chain is a necessary condition for the existence of a unique stationary distribution.
- Researchers have been studying the ergodicity of chaotic systems, which exhibit unpredictable behavior despite being deterministic.
- The ergodicity of a stochastic process can be verified by checking if the system's autocorrelation function decays to zero as time increases.