Editing Mixing (mathematics) (section)

{{Short description|Mathematical description of mixing substances}}
[[File:Baker's map mixing.gif|thumb|275px|Repeated application of the [[baker's map]] to points colored red and blue, initially separated. The baker's map is mixing, shown by the red and blue points being completely mixed after several iterations.]]

In [[mathematics]], '''mixing''' is an abstract concept originating from [[physics]]: the attempt to describe the irreversible [[thermodynamic process]] of [[mixing (physics)|mixing]] in the everyday world: e.g. mixing paint, mixing drinks, [[Mixing (process engineering)|industrial mixing]].

The concept appears in [[ergodic theory]]—the study of [[stochastic process]]es and [[measure-preserving dynamical system]]s. Several different definitions for mixing exist, including ''strong mixing'', ''weak mixing'' and ''topological mixing'', with the last not requiring a [[measure (mathematics)|measure]] 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 [[ergodicity]]: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" condition than ergodicity).