Far From Equilibrium

Equilibrium

In order to appreciate what we mean by 'far from equilibrium' we first need to start by understanding what is meant by 'equilibrium'. We can understand equilibrium using two examples: that of a pendulum, and that of a glass containing ice cubes and water.

If we set a pendulum in motion, it will oscillate back and forth, slowing down gradually, and coming 'to rest' in a position where it hangs vertically downwards. We would not expect the pendulum to rest sideways, nor to stand vertically from its fulcrum point.

We understand that the pendulum has expended its energy and now finds itself in the position where there is no energy - or competing forces -  left to be expended. The forces exerted upon it are that of gravity, and this causes the weight to hang low. The pendulum has arrived at the point where all acting forces have been canceled out : equilibrium.

Similarly, if we place ice cubes in a glass of water, we initially have a system (ice and water) where the water molecules within the system have very different states (solid and liquid). Over time, the water will cool slightly, while the ice will warm slightly (beginning to melt), and gradually we will arrive at a point in time when all the differences in the system will have cancelled out. Ignoring the temperature of the external environment, we can consider that all water molecules in the glass will come to be of the same temperature.

Again, we have a system where competing differences in the system are gradually smoothed out, until such time as the system arrives at a state where no change can occur: equilibrium.

In a complex system, we see very different dynamics: part of the strangeness of emergence arises from the idea that we might see ice spontaneously manifesting out of a glass of water! This is what we mean by 'far from equilibrium': systems that are constantly being driven away from the most neutral state (which would follow the second law of thermodynamics), towards states that are more complex or improbable. In order to understand how this can occur, we need to look at the flows that drive the system, and how these offer an ongoing input source that pushes the system away from equilibrium.

Example:

Lets take a look at one of our favorite examples, an ant colony seeking food. Lets start 100 ants off on a kitchen table (we left them there earlier when we were looking at Driving Flows. The ants begin to wander around the table, moving at random, looking for food. If there are crumbs on the table, then some ants will find them, and direct the colony towards food sources through the intermediary signal of pheromones. As we see trails form (a clear line forming out of randomness like an ice cube fusing itself out of a glass of water!), we observe the system moving far from equilibrium. But imagine instead that there is no food. The ants just keep moving at random. No emergence, nothing of statistical interest happening. When we remove the driving external flow (food) that is outside of the ant system itself then the ants become like our molecules of water in a glass. Moving around in neutral, random configurations.  Eventually, without food, the ants will die - arriving at an even more extreme form of equilibrium (and then decay)!

Origins

The phrase "far from equilibrium" was originally coined by Ilya Prigogine, and was used to characterize such phenomena as Benard Rolls (see also Prigogine & Stengers). Prigogine and Stengers were interested in how system that were driven by external inputs could gain order (as exhibited by the rolls), and how the increase in these external inputs could in turn drive order in increasingly interesting ways. 

Another way to say this is that systems in equilibrium lack energy inputs needing processing  whereas system from from equilibrium are characterized by having some kind of energy driver or differential at play.  

Muddying the Waters

While the above should now be somewhat clear, it is also true that complex systems, while indeed operating "far from equilibrium" can exhibit behaviors that imply a different kind of equilibrium: one that is not part of the domain of physics or chemistry but rather that of Game Theory (and economics). 

There are various multi-actor systems examined by Game Theorists and Economists, where actors (or agents) use competing strategies to see which will yield (or 'win') some form of allocation. Such games might be played once, to show optimum game choices, or multiple times, to see what occurs when past strategies plays a role in current strategies. Depending on how multiple agents deploy their strategies games might produce win/win outcomes (where multiple agents gain allocations),  win/lose outcomes (where my win results in your loss or vice versa), or lose/lose scenarios (where in efforts to outcompete one another, all agents wind up leaving empty handed). Game Theory can examine the kinds of strategies most viable for an individual agent in the system, but they can also analyze what strategies are most viable not solely for an individual agent, but for the collection gain of all agents in the system.

Such 'collective benefit' systems are described as being "Pareto efficient": and occur in instances when strategies result in dynamics whereby no agent can improve its own effectiveness without diminishing the effectiveness of the overall group. Another way to frame this is in terms of what would constitute a Pareto improvement: when system behavior can be enhanced in such a way that at least one agent is better off, and the system performance as a whole has not been made worse off by this change.

Example:

Imagine we are placing 100 trash cans in a park. We don't know where they should go, so we distribute them at random, but we add a few special features:

1. Each trash can has a sensor that can track how quickly it is filled

2. Each is also able to receive and relay a signal to its nearest neighbors - indicating its             rate of trash accumulation

3. Each is set on a rolling platform, that allowing it to navigate to a new location in the park.

Accordingly: the agent in the system is the trash can; the fitness criteria is gathering trash; the adaptive capacity is the ability to relocate; and the differential driving flows are the variable intensities of trash generation.

We can imagine this system to be driven now by simple rules: each trash can monitors, broadcasts, and receives information about its own rate of trash acquisition, as well as that of its nearest neighbors. At various time steps it makes a decision: remain in place or move - with movement direction weighted depending in accordance with more successful neighbors. Each movement entails a Pareto improvement.

It should be relatively intuitive to note that, over time, trash cans will move until such point as all cans are collecting identical amounts. At that point, the system has arrived at a Pareto Optima, where movement cannot occur without a reduction in overall system fitness (it should be noted that this state may only be a local optimum:  for more information). The system has calibrated itself to perform in the most effective way possible, restricted only by the scope of state spaces it was able to explore.*

* One proviso regarding this example is that the system may be  trapped in a local optima (see Fitness Landscape). As a result, the system above will function more effectively if individual agents occasionally engage in random search regardless of neighboring states. This allows potential untapped domains of trash production to be discovered and the recruited for.

The reason it is worth pointing out this particular dynamic, is that game theory often discusses such optimizing strategies as finding "Equilibria".  Accordingly, we have the famous "Nash Equilibrium" as a kind of game theory state (see the Prisoner's Dilemma Game), as well as other game theory protocols that use the term "Equilibrium" to refer to end states strategies. While we normally speak of "Pareto efficient" or "Pareto Optimum" rather than "Pareto Equilibrium", there is a notional slipperiness at work here, meaning that it is easy to think of complex systems as arriving at a kind of steady state where the system has found a kind of poised balance (as in the trash cans above). This kind of calibration and balancing act within their environment might be described as existing in a state of ecological equilibrium (rather than being far from it).

The muddiness comes from how the term is technically applied in physics or chemistry versus how it is used in economics and game theory. 

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