ergodicity Synonyms

No Synonyms and anytonyms found

ergodicity Meaning

Wordnet

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

  1. The ergodicity of a stochastic process implies that its time average is equal to its ensemble average.
  2. Ergodicity is a fundamental property of many physical systems, such as fluids and gases.
  3. 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.
  4. Ergodicity is a key concept in statistical mechanics and is used to derive many important results, such as the equipartition theorem.
  5. 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.
  6. Ergodicity is a powerful tool for studying the behavior of complex systems, such as climate and financial markets.
  7. Ergodic systems are often characterized by their mixing properties, which determine how quickly the system forgets its initial state.
  8. Ergodicity is a fundamental assumption in many areas of physics and engineering, such as statistical mechanics, fluid dynamics, and thermodynamics.
  9. The concept of ergodicity has also been extended to quantum mechanics, where it is known as quantum ergodicity.
  10. 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.