Self-organization laws

The most important property of the self-organized critical state is the presence of locally connected domains of all sizes. Since a given perturbation of the state 77 can lead to anything from a trivial one-site shift to a lattice-wide avalanche, there are no characteristic length scales in the system. Bak, et al. [bak87] have, in fact, found that the distribution function D s) of domains of size s obeys the power law... 

At first sight, self-organization appears to violate the Second Law of Thermodynamics, which asserts that the entropy S of an isolated system never decreases (or, more formally, > 0) see figure 11.2-a. Since entropy is essentially a measure of the degree of disorder in a system, the Second Law is usually interpreted to mean that an isolated system will become increasingly more disordered with time. How, then, can structure emerge after a system has had a chance to evolve ... 

Upon closer examination, we see that self-organization in complex system does not really violate the Second Law. The reason is that the Second Law requires a system to be isolated that is, it must not exchange energy or matter with its environment. 

P should also minimize distinction.s between conventionally distinct but atomic. primitives (such as space, mass, time, etc.). The vision is to take one more step along the metaphoric road remove jnan from the center of the universe —> remove all privileged frames of reference —> remove all absolutes —> remove all distinction between space and matter—r remove all distinction ( ) Start by eliminating the tacit assumption that whatever physics is self-organizing itself out of the soup of the current crop of physicists is the physics of this universe in short, go from a solipsistic phys-ics to a fundamentally relativistic physics, wherein even physics itself becomes a set (an infinite hierarchical set ) of self-consistent world-views rather than a prescribed set of exactly/uniquely prescribed laws operating independently of all observers. 

Self-organization seems to be counterintuitive, since the order that is generated challenges the paradigm of increasing disorder based on the second law of thermodynamics. In statistical thermodynamics, entropy is the number of possible microstates for a macroscopic state. Since, in an ordered state, the number of possible microstates is smaller than for a more disordered state, it follows that a self-organized system has a lower entropy. However, the two need not contradict each other it is possible to reduce the entropy in a part of a system while it increases in another. A few of the system s macroscopic degrees of freedom can become more ordered at the expense of microscopic disorder. This is valid even for isolated, closed systems. Eurthermore, in an open system, the entropy production can be transferred to the environment, so that here even the overall entropy in the entire system can be reduced. 

It is, however, possible—apparently in disagreement with the second law of thermodynamics—that order can be formed from disorder in a system, for example by means of self-organization processes in many cases, these have been observed experimentally. This order, however, is formed at the expense of an increase in disorder outside the system under observation order is pumped out of the system which is striving to reach an ordered state. Thus, disorder increases outside the system, and the second law is still valid. 

Section we show that presence of two such intermediate stages is more than enough for the self-organization manifestation. Lotka [22] was the first to demonstrate theoretically that the concentration oscillations could be in principle described in terms of a simplest kinetic scheme based on the law of mass action [4], Its scheme given by (2.1.21) is similar to that of the Lotka-Volterra model, equation (2.1.27). The only difference is the mechanism of creation of particles A unlike the reproduction by division, E + A - 2A, due to the autocatalysis, a simpler reproduction law E —> A with a constant birth rate of A s holds here. Note that analogous mechanism was studied by us above for the A + B — B and A + B — 0 reactions (Chapter 7). 

Instead of disintegration of the initial state we find that the law in Eq.(23) leads to increasing (self)-organization during a finite number of life times x. It is in this context that we will speak of microscopic selforganization in what follows below. As we need a more detailed description we will proceed to discuss the density operator concept in general and the reduced density matrices in particular. 

The committee surveyed the inventory of environments in the solar system and asked which non-Earth ones might be suited to fife of the terran type. Such locales are few, unless there are laws not now understood that could govern the early stages of the self-organization of biochemical structures and processes that could lead inevitably to evolving life forms.15 Subsurface Mars and the putative sub-ice oceans of the Galilean satellites are the only locales in the solar system (other than Earth itself) that are clearly compatible with terran biochemistry. 

Kauffman, S.A. 1995. At Home in the Universe The Search for Laws of Self-organization and Complexity. Oxford University Press, New York. 

Under the direction of the chief compliance officer and the corporate compliance committee, each organization should develop written compliance policies that pertain to the organization s practices that may be at risk for noncompliance. The policy should clearly delineate the organization s commitment to comply with all federal and state standards, with an emphasis on preventing fraud and abuse. The compliance plan should address, at a minimum, the False Claims Act, the Anti-kickback Statutes, physician self-referral laws, and laws regarding bribery and improper gifts. Once the plan is developed, it should be reviewed and approved by the organization s board of directors. 

The vast body of literature on electrochemical oscillations has revealed a quite surprising fact dynamic instabilities, manifesting themselves, for example, in bistable or oscillatory reaction rates, occur in nearly every electrochemical reaction under appropriate conditions. An impressive compilation of all the relevant papers up to 1993 can be found in a review article by Hudson and Tsotsis. This finding naturally raises the question of whether there are common principles governing pattern formation in electrochemical systems. In other words, are there universal mechanisms leading to self-organization phenomena in systems with completely different chemical compositions, and thus also distinct rate laws ... 

Knyazeva, E. N. and Kurdyumov, S. P., Laws of Evolution and Self-organization for Complex Systems, Nauka, Moscow, 1994 [in Russian],... 

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