Vol. 1. No. 1 Society 1.1 - Thermodynamics
The micro level
So we imagine a large number of simple particles, atoms or molecules, moving around in some space. To consider the simplest case, we assume that the forces of attraction between these particles are negligible. If we then follow the motion of any individual particle, we will see it undergoing a zigzag motion consisting of straight flights separated by rapid changes of direction. Each straight flight is the 'free flight' motion that takes place when no force is acting on the particle, and by Newton's first law of motion takes place at constant velocity. The rapid changes of direction, and of speed, occur when the particle collides with another particle. The repulsive force between the colliding particles changes the speeds and directions of both particles. (Billiard ball collisions provide a macroscopic example).
According to Newton's second law of motion, a force on a particle causes its velocity to change at a rate (called the acceleration) that is given by the strength of the force divided by the mass of the particle. The change in the velocity takes place in the direction of the force. A consequence of this law is the following: If we define the momentum of a particle as the product of its velocity and its mass, then the action of a force acting for a time is to change the momentum of the particle by an amount given by the product of the force and the time. (This product is called the impulse).
But, according to Newton's third law of motion, forces between particles are always mutual and equal in strength and opposite in direction. It follows that two colliding particles repel each other with forces of equal strength (and in opposite directions), and therefore change each other's momentum by equal amounts in opposite directions. Since momentum is a directional quantity (a so-called vector quantity), the sum of the momenta of the particles is the same after the collision as before. Total momentum is said to be 'conserved'.
Also conserved is the total energy. That is, the sum of the energies of the particles is the same after the collision as before. The energy of a stationary particle is called its internal energy, and is the energy of any and all actions taking place inside the 'particle'. The energy of a moving particle is the sum of its internal energy and the energy of its motion through space, its kinetic energy, which is equal to one half its mass times the square of its velocity. The amount of energy transferred from one of the colliding particles to the other is given by the product of the force times the distance over which the force acts. If the collision is not intense enough to cause changes inside the particles, their internal energies are not altered, and then the sum of the kinetic energies of the particles is the same after the collision as before.
If we also assume that collisions are not intense enough to destroy the particles (by breaking them into parts, for example), then the number of particles is always a conserved quantity. Collisions are then characterized by conservation of particle number, momentum, and of energy. If there are different types of particles (as in air), we give the number of each type in, say, a cubic inch of space. Alternatively, we can give the total mass of each type in a cubic inch. Either of these equivalent descriptions may be termed the matter content.
The macro level, conserved quantities
We now are in position to describe the leap from the micro to the macro, from the physics of the microlevel as a succession of particle free flights and collisions, to the macrolevel description of a gas consisting of a great many interacting particles.
We point out that in one cubic inch of normal air there are about four hundred billion billion (4x1020) molecules undergoing stereotypic actions - free flights of length of the order of a hundred thousandth (10-5) of an inch at speeds of the order of ten thousand (104) inches per second (about 700 miles per hour). The duration of each free flight is then about a billionth of a second (nano, 10-9). Each molecule makes about a billion collisions each second. (On the other hand, the collision duration in a gas is a small fraction of the free flight time).
The importance of the conserved quantities may now be understood. In spite of all the activity taking place in the cubic inch in each small time interval, all the collisions, all the changes in velocity of the individual particles, all the changes in their energies, the values of the conserved quantities are unaffected by the interactions occurring inside the cubic inch. The matter content is unchanged, the total momentum is unchanged, the total energy is unchanged. What happens is that the total momentum is distributed by the collisions among all the particles in the cubic inch in some characteristic manner. Similarly, the total energy is distributed among the kinetic energies of all the particles, and among the internal energies that are excited in collisions.
It should be noted that the same physical description would hold with air if one reduced the number of such molecules to a sparse collection of only a few handfuls in a cubic inch container, or in a very small container. The conclusions are valid for all sized boxes as long as each side is significantly longer than the free flight length (of 10-5 inch in normal air). It is that character of physics which will permit us to extend its scope to discussing more complex systems like living things in which a great number of internal actions will be found going on.
Local thermodynamic equilibrium
The key idea may now be stated: conditions inside the cubic inch are characterized and determined by the values of the conserved quantities. Two different cubic inches are macroscopically identical if they contain the same matter content (the number of molecules of each molecular type), the same momentum, and the same energy, even though one is here now and the other was half way round the globe and a century ago. The reason is that the molecular players have the same properties in both cases, they interact the same way in both cases, and the large number of these stereotypic interactions (e.g., collisions) among the players results in standard distributions of each conserved quantity among the individual players, the distributions being the same in both cubic inches. These standard distributions are called equilibrium distributions, and a small piece of the gas in which the equilibrium distribution is present is said to be in local thermodynamic equilibrium. Any deviation from the equilibrium distribution in a small piece is reduced very rapidly to zero by the stereotypical interactions inside the piece which act to share the conserved quantities among the players according to the equilibrium distribution. It is precisely this rapid drive toward local equilibrium that underlies the success and power of thermodynamics (macrophysics within and between organized levels).
When the total momentum of a small piece (such as our cubic inch) is zero, the piece is macroscopically at rest. When the total momentum is not zero, the piece is macroscopically in motion. The macroscopic velocity of the piece is equal to its momentum divided by its mass. Every small piece of still air is macroscopically at rest. Each small piece of windy air is in macroscopic motion, with different pieces generally moving with different velocities. What we have here is a macroscopic flow field.
The motional aspects of the situation illuminate the relation between the micro and macro levels of activity. The maroscopic velocity of a small piece is simply the directional (vector) average value of the velocities of all the microscopic players in the piece, each velocity being weighted by the mass of each player. Microscopically, there is a great deal of motion and action going on all the time, even in a piece that is macroscopically at rest. The velocities of the individual players in such a piece have the standard equilibrium distribution. In a piece that is in macroscopic motion, the same equilibrium distribution of microscopic velocities is present, but in addition there is also the common macroscopic velocity. If such a piece is observed by an observer moving along with it, it appears identical to a piece that is macroscopically at rest.
Thermodynamic coordinates and their relationships
The stereotypical interactions in a piece in local thermodynamic equilibrium give rise to a state of mechanical stress inside the piece. This stress is a mechanical measure of the intensity and frequency of the collisions taking place (the interactions that share the momentum among the players). The stress in a gas is called the pressure. It measures the average pressing force exerted (through collisions) by the players on one side of a square inch of area on the players on the other side of the same square inch. The pressure in a gas confined by a container is also the force exerted on each square inch of the container material (by collisions of the gas particles with the container walls).
Because the interactions share energy as well as momentum, there are also energy measures for the intensity of the local interactions.The direct measure is simply the energy per unit mass, or the energy per unit volume. A very important indirect, but more universal, measure is the temperature. Although temperature and the direct energy measure are closely related, the quantitative relation between them is different for different types of matter. Consider a macroscopically stationary piece of matter. When it is at its lowest possible temperature, absolute zero, it is at its lowest possible energy level, and its energy is called the zero-point energy. The energy of the piece increases as the temperature is raised. The excess of the energy above the zero-point energy is called the thermal excitation energy, or more simply, the heat energy. It is the heat energy that is distributed among the microscopic players according to the equilibrium distribution.
It is the temperature measure that determines which way heat energy flows when two pieces of matter are placed in contact. Heat energy flows from higher to lower temperature. (When a finger at normal temperature contacts a hot stove, there is a flow of heat energy from stove to finger, causing it to get hotter and its owner to pull away).
The quantities that describe the macroscopic properties of a small macroscopic piece of a gas that is in local thermodynamic equilibrium are then its matter content, its energy content, its temperature, and its pressure. The matter content may be given by the mass density (mass per unit volume) and the chemical composition (the fractions of each of the chemical species making up the matter content). The energy content may similarly be given by the energy density. The macroscopic describers are sometimes called the thermodynamic coordinates.
Because the equilibrium distribution of momentum and energy among the players is completely determined by the matter content and energy content (by the actual physical account of local thermodynamic equilibrium), these two describers determine the values of the temperature and pressure. As a result, there is a functional relationship among the matter content, energy content, and temperature. This relation is called the energy function. There is also a functional relationship among the matter content, energy content, and pressure. Eliminating the energy content from these two functional relationships provides the function relating the matter content, temperature, and pressure. This relation may be called the thermomechanical equation of state.
Although the stereotypical motions of the individual players is different in detail for liquids as compared to gases, the main thermodynamic (macroscopic) conclusions are basically the same. In liquids, the individual molecules are very close to each other, just about touching, the distance determined by a near balance between the (long range) forces of attraction and the (short range) forces of repulsion. In fact, condensed matter - liquids and solids - form because of the forces of attraction.
One aspect of the stereotypical motion of the individual molecules in a liquid may be described as follows: Each molecule is confined by a 'cage' of surrounding molecules, all of them in thermal fluctuational motion. The caged molecule bounces back and forth with its cage for many cycles, until a fluctuation occurs which opens up a 'hole' in the surrounding cage, allowing the caged molecule to make a 'hop' to an adjoining location and a new cage. In a gas, the molecules make long flights separated by short quick changes in velocity. In a liquid, they make relatively short hops separated by many shorter back and forth bounces within their cage.
The end results are much the same, with the same set of macroscopic descripters. The difference shows up in the details of the functional relations, the thermomechanical equation of state, and the energy function. (As an example, liquids are much more difficult to compress than gases).
Introduction to flow fields
A complete macroscopic description of a flow field may be made by dividing the entire space into small elements of volume, and giving the thermodynamic coordinates and the macroscopic velocity of each small volume. Such a description may be called a 'hydrodynamical description'.
Consider a large body of fluid that is macroscopically at rest. If the net force on each of its volume elements is zero, then each volume element remains macroscopically at rest, and the fluid is said to be in global mechanical equilibrium. If the forces that act on the volume elements are not in balance, then the net force on each volume element sets it into motion. Friction between adjacent layers of fluid that slip past each other then acts to stop the slipping and to bring the fluid back to rest in a new equilibrium state in which the forces are restored to balance.
If the temperature is uniform throughout, the fluid is said to be in global thermal equilibrium. In this state, there is no flow of heat energy between adjacent volume elements. If the temperature is not uniform, heat energy flows through the fluid directed from high temperature places toward low temperature places (The flow is said to be 'down the temperature gradient', the path of greatest change with distance). The heat flow acts to equalize the regional temperatures, to drive the whole system toward global thermal equilibrium.
If the matter content is uniform in all volume elements, with uniform concentrations of each molecular species throughout the fluid, then there is no diffusional flow of any molecular species from element to element, and the fluid is said to be in global chemical transport equilibrium. If a concentration of any molecular species is not uniform, there is a diffusional flow of that species down the concentration gradient from high to low concentration places. This diffusional flow acts to equalize the concentrations, to drive the system toward global chemical transport equilibrium. (This brief discussion of chemical equilibrium neglects the effect of forces that act differently on different molecular species. Such forces can act to produce equilibrium situations in which some species are more concentrated in one location, and other species in other locations. This can occur by the action of electric forces on ionic species, and even by the gravity force which acts to concentrate denser species in locations of lower altitude. Also not considered as yet is the possibility of chemical transformations by chemical reactions, which introduces the idea of reaction equilibrium).
The drive toward global thermodynamic equilibrium
What has just been described, in very concise fashion, are the kinds of motion of flow that takes place in flow fields, and the three kinds of drives - mechanical, thermal, chemical - that are always acting to move the system toward global thermodynamic equilibrium. The state of global thermodynamic equilibrium is characterized by a balance of forces on every volume element and no macroscopic motion of matter, uniform temperature throughout and no flow of heat energy, uniform concentration of each chemical species (or a balance of special species forces) and no diffusional flow of any particular species.
The macroscopic motion induced by net forces is convective momentum flow. It is more simply called convective motion or convection. The momentum (and the associated macroscopic kinetic energy) is carried or conveyed by the moving fluid. The heat energy flowing down the temperature gradient is a flow of heat energy through the fluid; the process is called heat conduction. Similarly, the diffusional flow of a particular chemical species is also a flow through the fluid. Two different chemical species can be diffusing in opposite directions (Diffusional flow generally refers to relative motion of different chemical species within a volume element of a fluid). Finally, the friction force between adjacent layers of fluid that are slipping past each other is accomplished by a non-convective momentum flow through the fluid, flowing from the higher speed fluid to the lower speed fluid. This process is called viscosity, more properly viscous diffusion.
The three non-convective flows or transports that take place throughout the fluid, those of heat energy down temperature gradients, particular chemical species down concentration gradients, and viscous momentum flow down slip-velocity gradients, are the mechanisms of the drive toward global thermodynamic equilibrium. In an isolated system, one closed by fixed walls that prevent the exchange of matter and of energy between the system and outside, these mechanisms invariably and inexorably drive the system toward global equilibrium. The time scale for the approach to global equilibrium depends on the size of the system, but is in any case a macroscopic time, as compared to the short time scale for achieving the local equilibrium distributions within any small volume element.
Commonality of the global equilibrium mechanisms
Although at first sight, the mechanisms of heat conduction, diffusion of chemical species, and viscosity appear to be different and independent, they all spring from the same process, the stereotypical fluctuational motion of the molecular players in the local equilibrium distribution.
To see this, focus attention on any imagined area inside a fluid. The molecules on each side of this area will, by virtue of their stereotypical fluctuational motions, do some crossing over to the other side of the area. This kind of 'diffusion mixing' across the common boundaries of adjacent volume elements acts to share and equalize the properties of the volume elements. If the fluid is hotter on one side of the area than the other, the diffusional mixing carries more energetic molecules into the hotter element, resulting in a transport of heat energy. Similarly, if a particular chemical species is more concentrated on one side of the area than the other, the diffusional mixing accomplished by the fluctuational motions of these molecules results in a diffusion transport. Finally, if the macroscopic velocity is larger on one side of the area than the other, the diffusional mixing carries molecules with larger macroscopic velocity into the region of smaller macroscopic velocity, and carries molecules with smaller macroscopic velocity into the region of larger macroscopic velocity, resulting in a momentum transport down the velocity gradient.
The mechanisms of heat conduction, diffusional flow, and viscous momentum flow, the three one-way drives toward global thermodynamic equilibrium, all arise from the combined action of a macroscopic gradient (of temperature, concentration, or slip velocity) and the diffusional mixing generated by the local stereotypical fluctuation of the molecular players.
Macroscopic action
We bring this lesson to a close with some remarks on the rich variety of processes that can occur in macroscopic flow fields. Consider first some of the ways that forces are exerted on volume elements of the field matter. Forces may be exerted by external agents such as the gravitational field of the Earth (this force is the weight of the volume element), by an external electric or magnetic field (when the matter has appropriate electrical or magnetic properties), or by a variety of other agents such as fan blades or paddles. Forces may also be exerted by a pressure gradient within the fluid itself, in which case a larger force is exerted on one side of a volume element than on the other side. The net pressure force on a volume element is directed down the pressure gradient, from high to lower pressure.
A simple example is that of a horizontal cylinder containing water confined between the closed end of the cylinder and a piston which is pushed against the water, thus pressurizing the water to a pressure that is higher than that of the surrounding atmosphere, 14.7 psi (pounds per square inch). If a small hole is made in the closed end of the cylinder, the water will squirt out at high speed, because the pressure exerted on each piece of water at the position of the hole is greater on the side facing the high pressure water than on the side facing the lower pressure air.
An example that involves two kinds of force is that of the atmosphere. Although the atmosphere is never macroscopically at rest, it is almost always fairly close to a balance of force on each of its volume elements. Small net forces result in large weather patterns. We may ask why the pressure at sea level is always fairly close to the value 14.7 psi. We may also ask why a piece of air that is located some distance above the ground or the ocean does not fall down. After all, Earth attracts all matter with a gravity force. The answer to the first question is that a vertical column erected on one square inch of the Earth's surface and extending all the way up to extremely high altitudes, contains an amount of air that weighs 14.7 pounds. The atmosphere is pressurized by its own weight, by gravity force. The answer to the second question follows from the answer to the first. The pressure at each altitude is simply the weight of the air sitting above one square inch at that altitude, and consequently is greatest at sea level and decreases to zero at higher and higher altitudes. There is then a net upward pressure force exerted on each piece of air, called the buoyant force (The buoyant force is the excess of the upward directed pressure force exerted on its bottom face over the downward directed pressure force exerted on its top face). The upward buoyant force due to the pressure gradient balances the gravity force.
The candle process
As a third example, consider an ordinary candle staying lit by the combustion of wax and oxygen at the tip of its wick. By its own action, the candle generates a steady supply of fresh oxygen-containing air (and a fresh supply of wax) at the wick tip. The heat generated by the chemical combustion process raises the temperature of the air in the flame cone. As a result, the air there expands, becomes less dense, and rises by buoyancy. As this leaves (by rising), the pressure is lowered, causing surrounding air to be forced inward toward the burning place. The local heating leads to a continued flow of air inward from the surroundings and upward above the burning place. By its own action, the candle generates this convection flow that ensures a steady supply of fresh air (At the same time, the heat of the flame melts the top of the candle, and molten wax climbs the wick - by capillary action - to the burning place That capillary action represents the action of another force system which will not be explained here at this time. In any, case, again by its own action, the candle ensures a continued supply of wax at the burning place).
The candle process occurs in many forms in many places in nature. It initiates atmospheric motion on the Earth. Solar energy is absorbed mostly at sea level (ground level), resulting in heating of the air at sea level. This leads to convective rising and roiling motions in the atmosphere. Convective roiling in the Earth's mantle is initiated by the heat in the Earth's core and the radioactive heat produced in the mantle, and is responsible for the motion of the Earth's plates. The heat energy, generated in the core of the Sun by (slow) nuclear fusion processes, is transported towards the surface first by heat conduction occurring via photons of light energy, but in the outer half of the Sun, the heat is carried to the surface by convective roiling, where it is radiated out as sunshine.
Adding to the Earth processes already mentioned - gravity, solar heating from without and the roiling within - the spinning of the Earth (which affects the motion of the atmosphere, the oceans, and the fluid parts of the Earth's interior), the process of phase change (evaporation, condensation, cloud formation, rain, snow, glaciation, melting and freezing), capillary action, and the process of chemical transformation via chemical reaction, leads to the rich geophysical - geochemical - biochemical evolutionary history of planet Earth.
Study of flow field processes demonstrates that the diversity of macroscopic action at all scales of activity is always enhanced by diversity of structure (heterogeneity) at all scales, and by diversity of forces and energy supplies. (Even though the basic physical forces in nature are few, the diversification of their effects by the various ways they combine is rather enormous).
This is illustrated by a final simple example, that of a coffee percolator in which a repeated 'chug' cycle occurs because of the central tube of the percolator. When a pot of water without a central tube is heated from below, the heat is transferred to the entire body of water by convectional roiling, resulting in boiling throughout the water (phase change from water to steam within the water). In a coffee percolator, the central tube (with its flanged bottom) is too narrow to allow roiling inside it. As a result, the water at the bottom of the tube remains in place and is heated steadily to the boiling point at which time it quickly boils into steam and erupts upward in a geyser of hot water and steam, a chug. This eruption shakes the central tube causing it to lose contact with the bottom of the pot, and cooler water from outside the tube enters to be heated again to the boiling point leading to the next chug cycle.
[Under the heading, "Life 1," an Essay entitled "What's wrong with EVOLUTION" is here in the original publication. The reference list below includes references cited in that paper. ]
Coda
[some browsers are not reading the symbols; therefore they each are labeled once in English]
Having begun a study of the theory of operation of all naturally working, self-organizing - viable - systems in the mid-60's (37), I began to realize that I had uncovered a new subject for physical study, the physics of complex systems, and that idea crept into the title of every paper I wrote from that time on. My colleagues and I put the name and concept of "homeokinetics" on that subject ((38,39). To us, homeokinetics, represents the dynamic regulation, internal and external, including self-organization and demise of complex systems in nature by thermodynamic - hierarchical - machinery and processes). I was pleased to find two formal physical measures for those field systems. They were field systems because their distributed interiors represented fields, separated from but operating within exterior world fields. These measures were a measure of condensation, the mechanical-thermodynamic bulk modulus, b , and the internalizing transport measure of bulk viscosity, l . The fantastic beauty of these two measures is that they furnish a space and time scale for such complex natural systems. If
b (beta)= bulk modulus
r (rho) = field density
C = propagation velocity in the field medium
l (lambda) = bulk viscosity
then
b /r = C2, l /r C = d , l /r C2 = t
t (tau) = the relaxation time constant of the field
d (delta) = the effective mean free path of the field
and if the bulk viscosity, l , is compared with the shear viscosity, m (mu), the transport measure of external momentum, their ratio is a measure of the internal complexity.
l /m = internal action / external-translational-action
(which is approximately equal to) internal time constant / external time constant
That is, it can be shown that the bulk to shear viscosity is the ratio of internal action within the system to the external, translational, action that appears out of the system (40). Action is the physical product of energy and time. That action ratio is essentially the internal time delay in action compared to the translational time delay, or external relaxation time. In complex systems, by our definition, that time ratio is very long.
To illustrate, so that it makes sense: A cookie going into your (or any) complex body, does not lose its energy, which is conserved thermodynamically, but compared to all other unit actions you undergo externally, it is long time delayed in its chemical transformations in your interior. That long time delay, because the interiors of complex systems are complex thermodynamic factories, is our notion of the hallmark of a complex system. To us, the physical issue is not the mathematical or logical complexity of a description of the system, but the complexity of internal action, which is defined by the relative time allotted to it.
Thus the measure of physical complexity of a field system composed of complex
atomistic-like entities is the factory day time scale of action of the
individual entities relative to the time scale of their interactive, relaxation
time movements.
Now biologist colleagues told me that they might accept this attempt at a physical - thermodynamic - modeling of complex fields such as the living system if and when it could get around to evolution and a physical theory for evolution. I replied that I considered that a fair challenge. I wish to show why I have been able to reply to that challenge with what I believe to be some measure of success.
First I want to make certain that the character of the bulk viscosity is understood. The shear viscosity is a measure of the transport of momentum, i.e., externalized momentum, carried by atomistic carriers from region to region. [Note or recall, that how momentum goes or changes is the hallmark of the Newtonian outlook]. The bulk viscosity is a measure of all other such transport. That can only be the transport into internal degrees of freedom of the atomistic-like entities. Chemical processes are identified by their reaction rate measures which are transport or diffusivity measures of chemical bond processes, e.g., the making, breaking, or exchanging of bonds between atomistic components.
Thus while chemistry is one kind of process that might be going on in the complex interiors of some atomistic fields, it is not the totality of such processes. Therefore complexity is not to be identified solely by the nature of chemical processes going on. The bulk viscosity is a much more inclusive measure of all internal processes going on in complex atomistic entities.
I make this point, because (a) the bulk viscosity - except for relatively simple kinds of rheological field entities, e.g., simple polymers or complexes - is still largely only viewed as a formal total measure of internal processing, yet (b) it can be shown - in simple cases - to have very interesting properties. For example it can be shown to augment the hydrostatic pressure. Thus in a simple gas, the hydrostatic pressure consists only of the momentum flux of atomistic units colliding - transferring or interchanging momentum - with each other or a wall; in a denser gas or liquid, in addition, there is a component from the longer range interatomistic forces of attraction or repulsion. In a high bulk viscosity field of atomistic components, there is a third component proportional to the bulk viscosity. That pressure component we have called the social pressure. It wells out from the interior of complex atomistic entities to equilibrate the pressure exerted by the environment on these entities. It is that component of pressure that makes complex systems look and act different from simple physical systems. It is responsible, for example, for their extensive memory functions, and the kind of external socializing processes that they enter into. That is why we have referred to our study of complex systems, in a catchphrase representation, as the study of nature, including life, Man, mind, and society. We have written extensively on such applications (41-44). Now finally it reaches more adequately up to biological evolution.
Here we see how the bulk viscosity transport process becomes involved in what is called Darwinian selection pressure, but now we see how it reaches farther out to the geophysics and geochemistry of Earth in creating a selection pressure on speciation as more of a Lamarkian-Darwinian evolutionary mix. The social pressure, emergent as a selection pressure, emerges hierarchically from the mixed actions of atomic nuclei, atoms, ions, molecules, macro molecules including genetic material, viruses and impacts on the internal actions of cells and multicellular organisms to drive speciation all within their geochemical-biochemical fields. Hopefully, now with this mechanism, physics and biology are reasonably joined.