ergodicity Synonyms
No Synonyms and anytonyms found
ergodicity Meaning
ergodicity (n)
an attribute of stochastic systems; generally, a system that tends in probability to a limiting form that is independent of the initial conditions
ergodicity Sentence Examples
- The ergodicity of a stochastic process implies that its time average is equal to its ensemble average.
- Ergodicity is a fundamental property of many physical systems, such as fluids and gases.
- The ergodic hypothesis states that the time average of a physical quantity over a long period of time is equal to its ensemble average over all possible states of the system.
- Ergodicity is a key concept in statistical mechanics and is used to derive many important results, such as the equipartition theorem.
- The ergodic theorem is a mathematical theorem that proves that the time average of a function of a random variable is equal to its expected value.
- Ergodicity is a powerful tool for studying the behavior of complex systems, such as climate and financial markets.
- Ergodic systems are often characterized by their mixing properties, which determine how quickly the system forgets its initial state.
- Ergodicity is a fundamental assumption in many areas of physics and engineering, such as statistical mechanics, fluid dynamics, and thermodynamics.
- The concept of ergodicity has also been extended to quantum mechanics, where it is known as quantum ergodicity.
- Ergodic theory is a branch of mathematics that studies the properties of ergodic systems.
FAQs About the word ergodicity
an attribute of stochastic systems; generally, a system that tends in probability to a limiting form that is independent of the initial conditions
No synonyms found.
No antonyms found.
The ergodicity of a stochastic process implies that its time average is equal to its ensemble average.
Ergodicity is a fundamental property of many physical systems, such as fluids and gases.
The ergodic hypothesis states that the time average of a physical quantity over a long period of time is equal to its ensemble average over all possible states of the system.
Ergodicity is a key concept in statistical mechanics and is used to derive many important results, such as the equipartition theorem.
