Quantitative and Physical History
Flows and Bubbles
By Mark Ciotola
First published on February 27, 2019
Many phenomena in both nature and society can be examined in terms of bubbles and flows. Many can be modeled as a combination of potential, flows, barriers and bubbles.
In the most general sense, a flow is the continuous transport of something from one place to another. In a more abstract sense, it is the continuous change of a quantity. For a short amount of time, a flow can be caused by inertia. For longer periods, something must drive the flow.
The consumption of potential can drive a flow. Then the flow can be said to contribute to the achievement of the potential. The flow can continue indefinitely as long as both the potential and that which flows are both steadily replenished. For many purposes, a flow can be viewed as a the result of a continuous supply of potential.
The shining of the Sun on the Earth in cold space is a continuous flow of energy that has lasted billions of years. The current of water down the Nile River is another flow that has lasted thousands of years.
The current of water down the Nile River is another flow generated by a gravitational force. Let us examine this. Water flows from higher elevations to lower ones, such as via the Nile. Water in highlands represent a higher gravitational potential than water at sea level. Water flowing downhill consumes (achieves) this potential.
Yet the Nile has been flowing for many thousands of years. How does the water at the high elevations get replenished? Atmospheric storm systems represent complex structures to dissipate potential. Sunlight places powerful amounts of energy at the surface of the oceans and wet land. Storms form to pump this energy more quickly away from the surface into the cold upper atmosphere. The transport of water into the atmosphere and its rain on the Earth’s surface increases the rate of energy transport. (Condensing water vapor in the upper atmosphere releases prodigious amounts of energy into outer space).
Resource and Economic Flows
There are also many physical flows in our economy. The transport of food from farm to city and of mineral from mine to factory represent flows.
Generalizing the Emergence of Structures
We discussed how regimes can emerge from civilizations as dissipative structures to increase entropy production. Here, we generalize the concept of a regime.
Formation of Bubbles
Bubbles emerge when a flow gets blocked. As potential builds up, the force against the blockage increases. Eventually the accumulation and force become so large that the blockage can no longer impede the flow. At this point, the blockage might be partially overcome, or it might become catastrophically destroyed. This is analogous to the formation and popping of a bubble. Another term for blockage is “Logjam”.
Emergence of Exponential Structures
In the case of a flow, heat engines will exponentially grow until they reach a limiting efficiency. Heat engine population and entropy production will reach a limit called a carrying capacity.
Heat engines begetting heat engines results in exponential growth in both quantity of heat engines and entropy production. Where the magnitude of potential is fixed, as entropy is produced, the potential decreases. As potential decreases the efficiency of the heat engines decreases. This decrease in efficiency comprises a limiting factor.
This decreased efficiency decreases the ability of heat engines to do work. Eventually, the total amount of both work and entropy production will decrease. Less work will be available to beget heat engines. If the heat engines require work to be maintained, the number of functioning heat engines will decline. Irreplaceable potential entropy continues to decrease as it gets consumed. Eventually, the potential entropy will be completely consumed, and both work and entropy production will cease.
As this scenario begins, proceeds and ends, a dissipative structure (a literal thermodynamic “bubble”) forms, grows, possibly shrinks and eventually disappears. Entropy production versus time can often be graphed as a roughly bell-shaped curve, giving a graphic illusion of a rising bubble.
Bubbles Involving Life
Populations of living organisms can experience thermodynamics bubbles. A bacteria colony placed in a media dish full of nutrients faces a potential of fixed magnitude. Each bacterium fills the role of a heat engine, producing both work and entropy. The bacteria reproduce exponentially, increasing the consumption of potential entropy exponentially. Eventually, it becomes increasingly difficult for the bacteria to locate nutrients, decreasing their efficiency. As efficiency decreases, the bacteria will reproduce at a slower rate and eventually stop functioning.
Ultimately, all potentials are fixed in magnitude. Possibly, the entire Big Bang and its progression could be viewed as a bubble. In practice, many potentials are renewable to a limited extent. For example, as long as the Sun shines upon the Earth in cold space, a potential will exist there.
Series of Bubbles
As long as a system maintains the ability to produce new heat engines, then instead of a single bubble, there will be a series of bubbles over time. There are several reasons that systems form bubbles instead of maintaining a single flow. Chaos (in the mathematical sense) provides one reason. Another reason is that a series of bubbles may provide for an overall higher entropy production rate than a more steady, consistent rate of production. Heat engines in a bubble may be able to obtain much higher efficiency during a bubble than during steady state, so that the average production in a series of bubbles may be much higher than during a steady flow, despite the below average production between bubbles.
Overshoot and the Predator-Prey Cycle
Yet even in the case of a flow, the rate of replenishment will be limited. Yet the rate of engine reproduction may have continued beyond carrying capacity. This can be called overshoot, a systematic “momentum” in a sense. In this case, even the flow can be treated as a substantially fixed (or “conserved” in the physics sense) quantity. A thermodynamic bubble will form.
Another case such as predator-prey cycles can also form where overshoot occurs, where the population of a predator overshoots the available prey, reducing both the population of the predators and the prey, so that there are cycles where the population of the predator is always “reacting “ to the population of the prey. Predator-prey cycles can also be expressed in terms of flows, bubbles and efficiencies.
Notes and References