Mixing (mathematics)

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, mixing is an abstract concept originating from <a href="/facts/Physics/a7aH2y08">physics</a>: the attempt to describe the irreversible <a href="/facts/Thermodynamic_process/LkeddKcu">thermodynamic process</a> of <a href="/facts/Mixing_(physics)/Mlt6XFoK">mixing</a> in the everyday world: e.g. mixing paint, mixing drinks, <a href="/facts/Mixing_(process_engineering)/zvhBolV4">industrial mixing</a>.
The concept appears in <a href="/facts/Ergodic_theory/rkqCbIy0">ergodic theory</a>—the study of <a href="/facts/Stochastic_process/Ng1n1dnB">stochastic processes</a> and <a href="/facts/Measure-preserving_dynamical_system/acIdlpqt">measure-preserving dynamical systems</a>. Several different definitions for mixing exist, including strong mixing, weak mixing and topological mixing, with the last not requiring a <a href="/facts/Measure_(mathematics)/yCq7zlI4">measure</a> to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies <a href="/facts/Ergodicity/CKY3Gr9v">ergodicity</a>: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" condition than ergodicity).

Mixing (mathematics) open-in-new

Mixing (mathematics)