In physics, a dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined, according to at least one of several mathematical definitions. For example, a measure-preserving transformation T is said to be strong mixing if whenever A and B are any measurable sets and μ is the associated measure. Other definitions are possible, including weak mixing and topological mixing. Every mixing transformation is ergodic, but there are ergodic transformations which are not mixing.
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| - Mezcla (física) (es)
- Mixing (physics) (en)
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| - In physics, a dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined, according to at least one of several mathematical definitions. For example, a measure-preserving transformation T is said to be strong mixing if whenever A and B are any measurable sets and μ is the associated measure. Other definitions are possible, including weak mixing and topological mixing. Every mixing transformation is ergodic, but there are ergodic transformations which are not mixing. (en)
- En física, se dice que un sistema dinámico se mezcla si el espacio de fase del sistema se entrelaza fuertemente, de acuerdo con al menos una de varias definiciones matemáticas. Por ejemplo, una transformación T que se dice que es una si siempre que A y B son conjuntos mensurables y μ es la asociada. Otras definiciones son posibles, incluyendo y la . Cada transformación de mezcla es ergódica, pero hay transformaciones ergódicas que no se mezclan. (es)
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| - En física, se dice que un sistema dinámico se mezcla si el espacio de fase del sistema se entrelaza fuertemente, de acuerdo con al menos una de varias definiciones matemáticas. Por ejemplo, una transformación T que se dice que es una si siempre que A y B son conjuntos mensurables y μ es la asociada. Otras definiciones son posibles, incluyendo y la . Las definiciones matemáticas de la mezcla están destinadas a capturar la noción de mezcla física. Un ejemplo canónico es el Cuba libre: supongamos que un vaso inicialmente contiene 20% de ron (el conjunto A) y 80% de cola (el conjunto B) en regiones separadas. Después de agitar el vaso, cualquier región del vaso contiene aproximadamente 20% de ron. Además, la mezcla agitada es, en cierto sentido, inseparable: no importa dónde se mire, o cuán pequeña sea la región que se mire, se encontrará 80% de cola y 20% de ron. Cada transformación de mezcla es ergódica, pero hay transformaciones ergódicas que no se mezclan. (es)
- In physics, a dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined, according to at least one of several mathematical definitions. For example, a measure-preserving transformation T is said to be strong mixing if whenever A and B are any measurable sets and μ is the associated measure. Other definitions are possible, including weak mixing and topological mixing. The mathematical definition of mixing is meant to capture the notion of physical mixing. A canonical example is the Cuba libre: suppose one is adding rum (the set A) to a glass of cola. After stirring the glass, the bottom half of the glass (the set B) will contain rum, and it will be in equal proportion as it is elsewhere in the glass. The mixing is uniform: no matter which region B one looks at, some of A will be in that region. A far more detailed, but still informal description of mixing can be found in the article on mixing (mathematics). Every mixing transformation is ergodic, but there are ergodic transformations which are not mixing. (en)
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