Editing Dissipative system (section)

== Overview ==
A [[Dissipation|dissipative]] structure is characterized by the spontaneous appearance of symmetry breaking ([[anisotropy]]) and the formation of complex, sometimes [[Chaos theory|chaotic]], structures where interacting particles exhibit long range correlations.  Examples in everyday life include [[convection]], [[turbulence|turbulent flow]], [[cyclone]]s, [[Tropical cyclone|hurricane]]s and [[life|living organisms]]. Less common examples include [[laser]]s, [[Bénard cells]], [[droplet cluster]], and the [[Belousov–Zhabotinsky reaction]].<ref>{{cite journal|last1=Li|first1=HP|title=Dissipative Belousov–Zhabotinsky reaction in unstable micropyretic synthesis|journal=Current Opinion in Chemical Engineering|date=February 2014|volume=3|pages=1–6|doi=10.1016/j.coche.2013.08.007|bibcode=2014COCE....3....1L }}</ref>

One way of mathematically modeling a dissipative system is given in the article on ''[[wandering set]]s'': it involves the action of a [[group (mathematics)|group]] on a [[measure (mathematics)|measurable set]].

Dissipative systems can also be used as a tool to study economic systems and [[complex systems]].<ref>{{Cite book|title = The Unity of Science and Economics: A New Foundation of Economic Theory|last = Chen|first = Jing|publisher = Springer|year = 2015|url=https://www.springer.com/us/book/9781493934645}}</ref> For example, a dissipative system involving [[self-assembly]] of nanowires has been used as a model to understand the relationship between entropy generation and the robustness of biological systems.<ref>{{cite journal|last1=Hubler|first1=Alfred|last2=Belkin|first2=Andrey|last3=Bezryadin|first3=Alexey|title=Noise induced phase transition between maximum entropy production structures and minimum entropy production structures?|journal=Complexity|date=2 January 2015|volume=20|issue=3|pages=8–11|doi=10.1002/cplx.21639|bibcode=2015Cmplx..20c...8H}}</ref>

The [[Hopf decomposition]] states that [[dynamical system]]s can be decomposed into a conservative and a dissipative part; more precisely, it states that every [[measure space]] with a [[conservative system|non-singular transformation]] can be decomposed into an invariant [[conservative system|conservative set]] and an invariant dissipative set.