Self-organization

The hypothesis about streamlining in the system due to its internal dynamics was expressed by the philosopher R. Descartes in the fifth part of The Discourse on the Method. He later elaborated this idea in detail in the unpublished book “Le Monde”.

I. Kant put forward a nebular hypothesis , according to which planets were formed from nebula due to the attraction and repulsion inherent in matter ^[1] .

It should be noted that the ideas about the spontaneous emergence of order and self-organization are not identical. Atomism of Democritus or Boltzmann statistics consider the emergence of order as an accident, and the category of order is subjective, the presence of order is apparent.

In 1947, the term appeared in the scientific publication of William Ashby ( eng. WR Ashby ) "Principles of the Self-Organizing Dynamic System" ^[2] . In the 1960s, the term was used in systems theory , and in the 1970s and 1980s it was used in the physics of complex systems .

G. Haken - the founder of synergetics defined it as the science of self-organization. Until the 21st century, synergetic seemed to be a monopolist on the description of self-organization. In connection with the cooperation of representatives of the natural sciences in the field of nanotechnology, it turned out that the term self-organization in the field of supramolecular chemistry and evolutionary biology is defined differently for other phenomena than in synergetics. In addition, the definition given in the framework of synergetics, thanks to the interdisciplinary nature of this science, has spread across different disciplines , has become fuzzy.

The definition given by G. Hacken in the 1980s. within the framework of synergy:

"Self-organization is the process of ordering (spatial, temporal or spatial-temporal) in an open system, due to the coordinated interaction of the set of elements of its components."

System Features:

• open (availability of energy / substance exchange with the environment);
• contains an unlimited number of elements (subsystems);
• there is a stationary stable mode of the system in which the elements interact chaotically (incoherently).

Process characteristics:

• intensive exchange of energy / matter with the environment, and completely randomly (without causing ordering in the system);
• the macroscopic behavior of the system is described by several quantities — the order parameter and the control parameters (the information overload of the system disappears);
• there is a certain critical value of the control parameter (associated with the energy / substance input), in which the system spontaneously enters a new ordered state (transition to a strong disequilibrium);
• The new state is due to the coordinated ( coherent ) behavior of the elements of the system, the effect of ordering is found only at the macroscopic level;
• A new state exists only with a non-stop flow of energy / matter into the system. With an increase in the exchange rate, the system goes through a series of the following critical transitions; As a result, the structure becomes more complex up to the onset of turbulent chaos.

For the uniqueness of the definition of the term, its connection with the characteristics of the system and process, as a rule, reference is made to one of three standard examples of self-organization:

• laser - spatial ordering;
• Rayleigh-Benard cells — spatial ordering;
• Belousov-Zhabotinsky reaction - spatio-temporal ordering;

The Nobel laureate Ilya Prigogine created a non-linear model of the Belousov-Zhabotinsky reaction, the so-called Brusselator . Since the emergence of ordering in such systems requires an influx of energy or an outflow of entropy, its dissipation, Prigogine called these systems dissipative . Due to nonlinearity , the presence of more than one steady state in these systems, neither the second law of thermodynamics nor Prigogine ’s theorem on the minimum rate of entropy production holds in them. However, there are examples of space-time dissipative structures — laminar combustion autowaves and heat waves (autowaves) in the fixed catalyst layer, for which the complete entropy production in the system is a functional of the autowave solution (Lyapunov thermodynamic function). And its minimum corresponds to a physically meaningful solution of the problem ^[3] .

By analogy of the description of self-organizing systems with phase transitions, dissipative self-organization is called the phase transition in a nonequilibrium system .

Synergetic methods have been used in almost all scientific disciplines: from physics and chemistry to sociology and philology . Grad formation and neural networks are described as dissipative structures . Recently, the use of the initially necessary mathematical apparatus of nonlinear equations has practically disappeared. This led to the fact that any system of natural origin, not belonging to the competence of equilibrium thermodynamics , was considered as self-organized.

In 1987, another Nobel laureate, Jean-Marie Len , founder of supramolecular chemistry, introduced terms "self-organization" and " self-assembly ", due to the need to describe the phenomena of ordering in the systems of high - molecular compounds under equilibrium conditions, in particular the formation of DNA .

The study of substances in the nanostate , the formation of a complex structure in the crystallization process without external influence also required the description of these phenomena as self-organization. But, in contrast to the synergistic approach, these phenomena occur in conditions close to thermodynamic equilibrium .

Thus, equilibrium phase transitions, such as crystallization, also turned out to be self-organizing. To eliminate confusion, the phenomenon of ordering in equilibrium conditions is often defined as conservative self-organization.

The concept of evolutionary catalysis, developed by A. P. Rudenko , is an alternative concept of self-organization for biological systems. In contrast to coherent self-organization in dissipative systems with a large number of elements (macrosystems), continuous self-organization is considered for individual (micro) systems. In the framework of this approach, it is determined that self-organization as a system self-development occurs due to internal useful work against equilibrium. Progressive evolution with natural selection is possible only as self-development of the continual self-organization of individual systems.

• Flowing wedge effect
• Columnar separation of basalts
• The reaction of Belousov - Zhabotinsky

• Methods for assessing self-organization .
• Self-organization and synergy: ideas, approaches and prospects .
• Tretyakov Yu. D. Processes of self-organization in chemistry of materials .
• Flax J.-M. Supramolecular chemistry .
• A. P. Rudenko. The Theory of Self-Development of Open Catalytic Systems. - M .: Publishing House of Moscow State University, 1969. - 276 p.
• A. Rudenko. Self-organization and synergetics .
• Shcherbakov A.S. Self-organization of matter in inanimate nature (Philosophical aspects of synergetics). - M .: Publishing House of Moscow State University, 1990. - 110 p.
• Melnik L. G. Theory of Systems Development: monograph / L. G. Melnik. - Sumy: University Book, 2016. - 416 p.