Mixing (physics)
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 definitions of mixing are meant to capture the notion of physical mixing. A canonical example is the Cuba libre: suppose that a glass initially contains 20% rum (the set A) and 80% cola (the set B) in separate regions. After stirring the glass, any region of the glass contains approximately 20% rum. Furthermore, the stirred mixture is in a certain sense inseparable: no matter where one looks, or how small a region one looks at, one will find 80% cola and 20% rum.
Every mixing transformation is ergodic, but there are ergodic transformations which are not mixing.
Read more about Mixing (physics): Physical Mixing
Famous quotes containing the word mixing:
“It was not till the middle of the second dance, when, from some pauses in the movement wherein they all seemed to look up, I fancied I could distinguish an elevation of spirit different from that which is the cause or the effect of simple jollity.—In a word, I thought I beheld Religion mixing in the dance.”
—Laurence Sterne (1713–1768)