Bull. 2 May 10, 1997
A Course of Study on Homeokinetics:
The Physics of Complex Systems
Principles and Applications
Arthur S. Iberall
In these series of lectures, we want to get to two great antinomies:
Ř Is there a physical science for the biological system without vitalistic undertones?
Ř Is there a physical science for the human social system with ‘explanatory’ and ‘predictive’ power?
However, language is a very entangling web, loaded with meaning. It almost requires a thick book of unpacking for each word. That, in part, is the dilemma we face in an exposition of homeokinetics as a physics for complex systems. As a start, we lay out seven definitions and principles, and then describe a simple application of the principles in the modeling of a living system. With further extensions, this approach can be used to model social systems for modern humans.
1. Science: Parsimonious, principled, systematic, and predictive description of things in nature.
2. System: A bounded group of related formal, functional, or mentally constituted units that make up a unified whole (e.g., the world system; a philosophic system).
3. Physical science: First among sciences, it deals with the laws of movement and change in space and time in all material-energetic systems, under the action of forces. Not only are the systems bounded, but their units are atomistic. Thus, intrinsically, a micro and macro level of description exists in all physical systems, and it is necessary to relate them.
4. Key horizontal reductionism for physical science: The principles of physics stand off to one side; on a second side stands a nested hierarchy of the systems in nature. As currently understood, that hierarchy comprises:
Ř The universe
Ř Intragalactic systems, including gas clouds, dust clouds, stars, planets, planetismals, also planetary subsystems including geochemical, biochemical, life, and society
Ř A physical vacuum (An earlier age thought it to be turtles all the way down).
The two sides are connected by strategies. The corpus of physics consists of its pure principles and its hyphenated applications, e.g., cosmological physics, stellar physics, biophysics, social physics, nuclear physics, geophysics.
5. Modelling methodology for physical systems: A force bounding enclosure is identified. Within that enclosure, a heterogeneous assemblage of atomistic units that can resist destruction are depicted. The system is developed through the character of the interactions under available forces of the atomistic units. Chemistry, for example, is the making, breaking, and exchanging of force-developed bonds among the units. There are only a very few basic forces. Systems emerge from the cooperation between attractive and repulsive forces. The atomistic units are in sustained motion. A physics of systems emerges basically from the capability to identify a limited number of process variables that are conserved by the interactive atomistic units during their interactions.
6. Modelling simple physical systems: In a simple ensemble system or collective with interactions by particle pairs under mechanical forces, the units exhibit conservations of:
Ř momentum, and
With electrical forces, there is conservation also of:
Ř electric charge.
The continuing paired interactions quickly equipartition energy among all the atomistic players, resulting in a local regional equation of state at a macroscopic level (transforming microscopic measures of mass, momentum, and energy to macroscopic measures of mass density, pressure, and energy density or temperature which measures energy density per degree of freedom of movement. The equation of state is their interrelation). Besides equilibrium field processes described by an equation of state, there are near equilibrium steady flow and transient flow processes that can be described by equations of change. Such equations describe both:
Ř smooth or laminar flow fields, or
Ř turbulent and eddying flow fields
This description is good enough to deal with almost all flow processes in the universe such as the big bang expansion of the universe, motion in galaxies, in stars, in planetary plastic or fluid processes, such as magma, waters, and atmosphere, blood flow, water and air transport systems, chemical flows. Extending solid state processes beyond their elastic limits also represents describable flow processes.
7. Modeling complex physical systems: In a complex ensemble or collective system, given that a persistent system emerges, there is a longer period of time rather than a few atomistic interactions, for which a near local equilibrium emerges. Our homeokinetic definition of a complex system is a system which exhibits extremely long time delay in their complex atomistic interiors. By this definition, a near equilibrium emerges in what we call “the factory day” of the atomistic units. There is nothing physically strange in the atomistic interactions. It is just that these interiors can be represented as internal fluid factories. The living organism, or the mass units in a complex atmosphere, exhibit such fluid complexity. A morsel of food enters the factory and it undergoes a great number of time delaying internal transformations; or energy is tied up in a metastable water bearing cloud. The conservations in such systems are somewhat transformed. Instead of only one mass conservation, there is a conservation of a number of mass species, allowing for chemistry via the electric force; there is the conservation of energy; but the conservation of momentum transforms into the conservation of action (the organized more macroscopic emergence of energy-time products from the complex unit factories - their ‘actions’). The physical principle underlying the transformation is like Bohr’s early quantum theory. In that theory, the mechanics of any fundamental particle interaction can be described by the following cycling form:
Ř The sum of momentum-displacement product interactions is measured by a small number of units of a fundamental ‘natural’ constant of action, Planck’s constant h.
Our macroscopic form of that principle is that an energy dissipating complex field unit expends a unit of factory day action which is characteristic of the complex atomistic species (note that according to the first law of thermodynamics, energy in the physical universe is neither created nor destroyed; but according to the second law it may be transformed dissipatively into lower, more degraded forms of energy). We have scaled that measure H for all mammals. It varies with the 0.80 power of adult body mass; illustratively, about 2,000 kcal-days of action per day for humans.
8. Modelling a living system: We will apply these principles to a living collective -- the simplest -- a colony of flagellated bacteria. A complex living system adds what we may perceive to be one more conservation, the conservation of population number. Since living atomistic units are born and die, and by thermodynamic reasoning they cannot reproduce to infinite number nor do they very
soon die out in normal reproducing time scales, we may assume that conservations of mass species and number separate (by directing the flow of material, we can raise many or few small or large plants or animals). Thus they represent independent components of the equations of state or change. We propose to show, in an indefinitely maintained flow field, that the equation of state of such a near steady flow field colony requires a relation among four conservations, flows for:
Ř mass species
Ř energy, and
Note that a system was characterized as a bounded group of units organized into a field collective. That bounding may have been achieved by solid walls, elastic walls, an ingathering gravitational force, actually any force that would turn the movement inward by acting as a centering force. Here we will use the bacteria’s own action spectrum to center their spatial location.
What is proposed is to maintain a single species colony of say 10,000 live bacteria in a particular region in a flow system. Take a U-tube and arrange a steady drip of water into that tube so that it overflows out in the exit end, say at a level a little lower than at the entrance end. By changing the difference in height, we can adjust to any velocity flow field that we wish to elect. Our proposal is to maintain a colony of bacteria in the entrance region of the tube at a definite number level. However, we propose to make them work at some reachable energy consumption level within their competence. That is why we have adjusted the velocity of the field. We propose to make them swim at that speed.
The external modes of action of flagellated bacteria are:
Ř ingest food,
Ř swim in a straight line by rotating their flagella one preferred way, and
Ř tumble in motion by reversing that flagellar motion.
The empirical findings are that in favorable media, the straight line segments are longer. The resultant motion is an apparent diffusion up a favorable food gradient. In addition, there is a division period in which the bacteria divide in half (double their number) by reproductive fission. That time scale depends on temperature. A common temperature range is somewhere between near freezing and boiling water temperatures. A typical doubling time at room temperature may be in the vicinity of, say, 20 minutes. Thus one elects some in-between temperature to thermostat the flow system.
We have to know the energy consumption of our selected bacterial species when swimming in a stream of our elected velocity at our given temperature. We can perform tests on a small sample to determine that specific consumption, or we might make a crude estimate from our mammalian data. Such an estimate might come out in the vicinity of say 50 picograms (10-12 grams) per minute of glucose. So we add such a stream of glucose to our U-tube flow system.
What would happen if we put in one, a few, the number we wish to maintain, or many more of our desired bacteria? Obviously they would be swept along by the stream, but in the competition for the limited glucose supply:
(a) there would be continued growth and division, number doubling per 20 minutes, and
(b) by glucose depletion, there would form a gradient of glucose concentration in the stream, so that the more favorable region of occupancy is toward the entrance.
A diminishing exponential concentration would develop, concentrating the cell number up near the entrance. Is that the flow equilibrium resultant?
No, because the energy expenditure is for the dissipative cost of swimming. It does not supply the required material - proteins and nucleic acids - needed to maintain the bacterial body material growth supply. Thus, the doubling growth could not take place. Either the number growth would have to stop, or - if forced to continue - some cells would become moribund and die. Since they could not swim, they would be swept away.
Thus we see the additional conservation condition. To maintain a dilute non-interacting colony of say 10,000 bacteria, we have to supply the material replacement for the bacteria that die and are swept away. We must add to our stream the required material flux in protein or amino acids and nucleic acids that are disappearing. If the various streams are correct in magnitude, then when we introduce whatever number of the pure strain we wish to maintain, it will move by fission and death toward the equilibrium in number, in action, in mass flow streams, and in the energy stream that represents one point in the equation of state for those bacteria at that operating temperature, with no unaccounted-for ingredients in the outflow. By repeating the experiment at different temperatures and velocities, etc., we can determine the entire mathematical relationship among the components of this four variable equation of state (This is as an idealized but realizable equation of state. There are some more dynamic unstable states for the bacterial processes which are possible, but we do not have to confront them in our first simple modeling). And then this can be done for other living species.