Ideas from statistical mechanics for the notion of infinite mixing.

Roughly speaking, mixing is the property of a dynamical system whereby
the dynamics tends to mix up , or randomize, trajectories. When a
finite reference measure exists, the natural formulation of mixing
coincides with the decay of correlations (in time) of the observables
of the system.
In the case of an infinite reference measure, the standard
definition--a.k.a. finite mixing--is inapplicable. Finding an
effective replacement--infinite mixing--is a fundamental, and debated,
question.
Virtually all the definitions that have been attempted so far use
local observables , that is, functions that essentially only see
finite portions of the phase space. We introduce the concept of
global observable , a function that gauges a certain quantity
throughout the phase space. This concept is based on the notion of
infinite-volume average, which is inspired by statistical mechanics
(which is, after all, the field of mathematical physics that has most
successfully dealt with extended systems).
Endowed with the notions of global and local observables, we give a
few definitions of infinite mixing. These fall in two categories:
global-global mixing, which expresses the decorrelation of two
global observables, and global-local mixing, where a global and a
local observable are considered instead.
We will discuss these definitions and, time permitting, see how they
function on some examples of infinite-measure-preserving dynamical
systems.