Open thermodynamic systems, under certain contexts (e.g. thermodynamic non-equilibrium) may reduce their entropy and spontaneously form structured collective behavior, that is, information, by undergoing phase transitions. This spontaneous formation of structures from a random, symmetric, homegeneous state is called self-organization or spontaneous pattern formation. It arises when the previously spatially homogenous, and thus symmetrical state, loses stability (becomes a repeller) and breaks the symmetry. The breaking of the symmetry of the homogenous state means formation of structure. The stable structure formed is the attractor state under the actual context. Of course, structures may change among them also through self-organization, if the context is being changed. Spontaneous formation of structures (or spontaneous pattern formation) is the oposite to formation of structures by design, such as text printing, or DVD burning, or cookie shaping by a cookie cutter. Externaly designed structures always need an externaly (usually by human beings) imposed pattern on the system.

Self-organizing structures use the energy-mass input from the environment and simultaneously disperse (dissipate) energy-mass into environment. What happens in between is a stable structure constrained by the immediate context. Such structures are called dissipative structures. If the input of mass-energy input is suppressed, the dissipative structure decays.

It is not hard to see that our bodies and their sub-systems (organs, tissues and cells) are dissipative structures, whose morphology and function are constrained by evolved genes and their expression, chemical species involved, natural and social environment etc..

Examples of self-organization in chemistry are extensive list of reactions , reaction-diffusion processes etc.

In biology, the morphogenesis , the heart ,  brain activity, the switch of locomotor patterns and movements . schools of fish , swarms of insects and crowds of people and flocks of birds  are examples of self-organization. The locomotor patterns and movements are also said to be soft-assembled, which means self-organized.

There are numerous examples of self-organization in geophysics: mantle convection, cloud formation and development , fire, jet streams , ocean currents , tropical cyclones and tornados . Self-organizing structures arise when the open thermodynamic system is being kept in a thermodynamic non-equilibrium.



Self-assembly occurs in systems which, contrary to self-organized dissipative structures, eventually attain their thermodynamic equilibrium states. For right context (e.g. sufficiently low temperature and relatively high density of components) very ordered structures may emerge under such context. These structures arise because the components (molecular  and supramolecular agregates create bonded states, and as such, form macroscopic collective structures. Examples are self-assembly of biological membranes, proteins , DNA, RNA, organelles, viruses, crystals etc.

Robert Hristovski 18.02.2019