Complex OutLaws!

For those who are haven't dusted off their high school science textbooks recently, it is worth a quick refresher on the 2nd law of thermo-dynamics. Initially formulated by Sadi Carnot in 1824 (he was looking at the flow of heat in steam engines), the law has been expressed in various technically precise ways. For our purposes, the importance characteristic of these definitions is the idea of loss of order. Any ordered system will eventually move towards disorder. There is no way of getting around it. Things get messy over time - that's the Second Law. Everything ultimately decays. You, me, the world, the universe.

We can contemplate the metaphysical implications of this (the 2nd law is a bit of a downer) over a cup of coffee, while watching this video. We see illustrated the sad,  inevitable decrease in the cream's order as it meets with coffee (it's pretty relaxing actually):

Cream dis-ordering as it enters coffee

What the 2nd Law states is that something is ultimately lost in every interaction, and because of that, more and more disorder is ultimately created. We can ask heat to do work in driving a steam engine, but some of the heat will always be lost in translation, so that even if we are able to produce localized work or order, more disorder has ultimately been created in the universe as a whole. We call this inevitable increase in disorder 'entropy'.

But wait - you say - there is order all around us! While this may appear true, it is because what appear to be violations of the 2nd Law are achieved within the boundaries of a particular system. While a particular system can gain order, it is only because its disorder is simultaneously being dissipated into the surrounding context. Local order (within the system) is thus maintained at the expense of global disorder (within the environment). Were the system to be fully closed from its context, it would be unable to maintain this local order.

Thus, the ability to increase order in violation of the 2nd Law is called Negentropy - and one of ways in which Negentropy can be generated is by creating a system that is 'open and dissipative': meaning that an energy source can flow in to drive order, and waste can flow out to dissipate disorder.

Example:

A famous example of this dynamic is in  Benard/Rayleigh convection Rolls (a phenomena studied by Prigogine & Stengers as an example of self-organizing behavior). In this example, we have fluid in a small Petri dish, heated by a source placed under the dish. The behavior of the fluid is the system that we wish to observe, but this system is not closed: it is open to the input of heat that traverses the boundary of the Petri dish. Further, while heat can 'get into' the system, it can also be lost to the air above as the fluid cools. Note that the overall system clearly has a defined 'inside'  (the fluid in the Petri dish), and a defined 'outside' (the surrounding environment and the the heat acting upon the Petri dish), but there is not full closure between the inside and outside. This is what is meant when we say that complex systems are Open / Dissipative . We understand them as bounded, (with relations primarily internal to that boundary), but nonetheless interacting in some way with their surroundings.  Were the boundary fully closed no increase in order could not occur.

Let us turn now to the flows driving the system. As heat is increased, the energy of this heat is transferred to the fluid, and the temperature differential between the top and the bottom of the liquid causes heated molecules to be driven upwards. At the same time, the force of gravity causes the cooler, molecules in the fluid to be driven downwards. Finally, the drag forces acting between rising and falling molecules cause their behaviors to become coordinated, resulting in 'roll' patterns associated with Benard convection.

Rayleigh/Benard Convection (fluid of oil/ silver paint)

The roll patterns that we observe are a pattern: a global structure that emerges from the interactions of many agitated molecules without being 'coordinated' by them. What helps drive this coordination is the dynamics of the interacting forces that the molecules are subjected to (driving heat flows and counteracting gravity pressures), as well as how the independent molecular responses to these pressures feedback to reinforce one another (through the drag forces exerted between molecules).  That said, the fluid molecules do nothing on their own absent the input of heat. Instead, heat is the flow that drives the system behavior. Further, as the intensity of this flow is amplified (more heat added), the behavior of the fluid shifts from that of regular roll patterns to more turbulent patterns.

Setting boundaries

Prigogine & Stengers were the first to highlight the importance of open dissipative structures in generating complexity dynamics. Earlier works in General Systems Theory (Ludwig V. Bertalanffy) attuned to the complex dynamics at work within an internal structure, but did not make a distinction between open and closed structures. Closed structures in contrast to open structures do not process new inputs, and therefore are unable to generate novelty.

At the same time, systems need some sort of boundary or structure so as to hold together components of enough collective identity that they can work in tandem to process flows. It is therefore important to determine what is the appropriate boundary of any complex system under study, and what kinds of flows are relevant in terms of crossing those boundaries. 

Often, complexity involves multiple overlapping systems, each with their own internal dynamics and external flows, but systems can become entangled as one systems exports become another's inputs. In order to simplify these dynamics, it is perhaps helpful to try to identify which groups of agents in a system belong to a particular class of that shares a common driving flow and then examine the dynamics with respect to only those flows and behaviors. Systems can then be layered onto systems to build a more complete understanding of the dynamics at play. 

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