Self-organization in the context of "Perturbation theory"

Living systems are life forms (or, more colloquially known as living things) treated as a system. They are said to be open self-organizing and said to interact with their environment. These systems are maintained by flows of information, energy and matter. Multiple theories of living systems have been proposed. Such theories attempt to map general principles for how all living systems work.

Earth system science (ESS) is the application of systems science to the Earth. In particular, it considers interactions and 'feedbacks', through material and energy fluxes, between the Earth's sub-systems' cycles, processes and "spheres"—atmosphere, hydrosphere, cryosphere, geosphere, pedosphere, lithosphere, biosphere, and even the magnetosphere—as well as the impact of human societies on these components. At its broadest scale, Earth system science brings together researchers across both the natural and social sciences, from fields including ecology, economics, geography, geology, glaciology, meteorology, oceanography, climatology, paleontology, sociology, and space science. Like the broader subject of systems science, Earth system science assumes a holistic view of the dynamic interaction between the Earth's spheres and their many constituent subsystems fluxes and processes, the resulting spatial organization and time evolution of these systems, and their variability, stability and instability. Subsets of Earth System science include systems geology and systems ecology, and many aspects of Earth System science are fundamental to the subjects of physical geography and climate science.

Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction. When the constitutive components are molecules, the process is termed molecular self-assembly.

Self-assembly can be classified as either static or dynamic. In static self-assembly, the ordered state forms as a system approaches equilibrium, reducing its free energy. However, in dynamic self-assembly, patterns of pre-existing components organized by specific local interactions are not commonly described as "self-assembled" by scientists in the associated disciplines. These structures are better described as "self-organized", although these terms are often used interchangeably.

A grassroots movement uses the people in a given district, region, or community as the basis for a political or social movement. Grassroots movements and organizations use collective action from volunteers at the local level to implement change at the local, regional, national, or international levels. Grassroots movements are associated with bottom-up, rather than top-down decision-making, and are sometimes considered more natural or spontaneous than more traditional power structures.

Grassroots movements, using self-organisation, encourage community members to contribute by taking responsibility and action for their community. Grassroots movements utilize a variety of strategies, from fundraising and registering voters, to simply encouraging political conversation. Goals of specific movements vary and change, but the movements are consistent in their focus on increasing mass participation in politics. These political movements may begin as small and at the local level, but grassroots politics, as Cornel West contends, are necessary in shaping progressive politics as they bring public attention to regional political concerns.

In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled (at atmospheric pressure) significantly below 0 °C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0 °C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay.

Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immediately.

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas.

Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, despite the deterministic nature of these systems, this does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:

Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous order" is typically used to describe the emergence of various kinds of social orders in human social networks from the behavior of a combination of self-interested individuals who are not intentionally trying to create order through planning. Proposed examples of systems which evolved through spontaneous order or self-organization include the evolution of life on Earth, language, crystal structure, the Internet, Wikipedia, and free market economy.

In economics and the social sciences, spontaneous order has been defined by Hayek as "the result of human actions, not of human design".

Democratic confederalism (Kurdish: Konfederalîzma demokratîk), also known as Kurdish communalism, Öcalanism, or Apoism, is a political concept theorized by Kurdistan Workers Party (PKK) leader Abdullah Öcalan about a system of democratic self-organization with the features of a confederation based on the principles of autonomy, direct democracy, political ecology, feminism ("Jineology"), multiculturalism, self-defense, self-governance and elements of a cooperative economy. Influenced by social ecology, libertarian municipalism, Middle Eastern history and general state theory [de], Öcalan presents the concept as a political solution to Kurdish national aspirations, as well as other fundamental problems in countries in the region deeply rooted in class society, and as a route to freedom and democratization for people around the world.

Although the liberation struggle of the PKK was originally guided by the prospect of creating a Kurdish nation state on a Marxist–Leninist basis, Öcalan became disillusioned with the nation-state model and state socialism. Influenced by ideas from Western thinkers such as the libertarian municipalist and former anarchist Murray Bookchin, Öcalan reformulated the political objectives of the Kurdish liberation movement, abandoning the old statist and centralizing socialist project for a radical and renewed proposal for a form of libertarian socialism that no longer aims at building an independent state separate from Turkey, but at establishing an autonomous, democratic and decentralized entity based on the ideas of democratic confederalism.