Physical Foundations of Self-organizing Systems

The appearance of coherent global pattern due to local interactions is known as self-organization. Self-organization is a~spontaneous~process in highly non-equilibrium dissipative systems that form structures which tend to maximize energy dissipation by leveling off energy gradients. This follows as a direct consequence of the Second Law of Thermodynamics. Also,~a local interaction~embodies in the above definition a mechanistic dimension to self-organization. The link between mechanics and the Second Law of Thermodynamics lie in the Principle of Least Action, a strong law of nature that is obeyed in every spontaneous process. Thus, self-organization rests on two basic foundational principles of nature namely, the Second Law of Thermodynamics and the Principle of Least Action. We attempt to develop a formal definition of self-organization based on those principles.