The statement of the second law appeared as a contradiction of the mechanical world view. In response, Boltzmann attempted to salvage the Newtonian (purposeless, mechanical) paradigm by reducing the second law to a stochastic collision function, to a law of probability. His move, by making the spontaneous production of order "infinitely improbable" and thus branding the second law as the "law of disorder," deflected attention from the profound insight of Thomson and Clausius.
Modeling gas molecules as billiard balls, Maxwell (1871) showed that nonequilibrium velocity distributions would become increasingly disordered with each collision leading to a final macroscopic state of uniformity and symmetry. Boltzmann recognized this state, in which the macroscopic uniformity and microscopic disorder corresponds to the minimization of all field potentials, as the state of maximum entropy and claimed that the second law was simply a result of the fact that disordered states caused by local stochastic collisions were the most probable. From this interpretation, molecules moving "at the same speed and in the same direction" (ordered behavior) was in Boltzmann's (1886/1974, p. 20) view, "the most improbable case conceivable ... an infinitely improbable configuration of energy." As emphasized in the two sections that follow, this view (still found in numerous textbooks) is precisely on its head: Rather than being infinitely improbable, the production of order is lawful and inexorable.
A PHYSICAL SELECTION PRINCIPLE
Classical thermodynamics tells us that entropy is maximized at thermodynamic equilibrium but tells us nothing about the path of action selected to get there. An answer to the question can be framed in terms of a simple experiment, the consequences of which show a physics that is not only end directed but inherently opportunistic in attaining its ends. Figure 3 shows an adiabatically sealed (closed to the flow of heat) chamber divided by an adiabatic wall into two compartffients, each holding equal quantities of a monatomic gas such that there is a temperature difference T, > TI1 producing a field potential with force F. If a section (labeled 1) of the adiabatic seal is stripped from the dividing wall (Figure 3a), an incoherent flow of energy or heat (a drain) is spontaneously produced rrom I to II until the potential is minimized (the entropy is maximized) given the constraints. The rate of entropy production is given by:
where dQIdt and (IIV -1/7") are the flow and force respectively. Equation (1) shows that, ceteris paribus, the rate of entropy production is determined by the coefficient of conductivity of the wall. Figure 3b depicts the removal of a second portion
|FIGURE 3 A simple experimental arrangement expressing the law of maximum entropy production. From "Order, Evolution and Natural Law: Fundamental Relations in Complex System neory" by R.Swenson, in C. Negoita (Ed.), Cyber-netics and Applied Systems (in press-c), New York: Dekker. Copyright 1991 Marcel Dekker, Inc. Reprinted by permission
(iabeled 2) of the adiabatic seal. The wall underneath in this second case is composed of a different material with a different coefficient of conductivity. If the rate of 2 relative to the rate of I is sufficient to drain some quantity of the potential before I drains it all, then that quantity is automatically assigned to 2. If, with different relative coefficients, 2 can drain all the potential before I can drain any, then the entire quantity is assigned to 2 and I gets none. With the adding of more drains (Figure 3c), the behavior is precisely the same: Regardless of the particulars of the system, not only will it produce the dynamics appropriate to achieving the same final state, but it will select the assembly of pathways or drains among the available dynamics so as to get to the final state (minimize the field potential or maximize the entropy) at the fastest possible rate given the constraints. The foregoing expresses the law of maximum entropy production, a universal selection principle that provides the physical basis for the inexorability of spontaneous, evolutionary ordering (Swenson, 1988, 1989b, 1989c, in press-b) which we discuss more fully below.
|FIGURE 4 Two time slices from the Benard experiment where (left) shows heat transer in the disordered regime and (right) shows heat transfer through the spontaneous production of order above the critical minimal field potential threshold. From "Emergent Attractors and the Law of Maximum Entropy Production: Foundations to a Theory of General Evolution" by R. Swenson, 1989b, Systems Research 6, p. 192. Copyright 1989 by Pergamon. Reprinted by permission.
THE INEXORABILITY AND OPPORTUNISM
OF ORDER PRODUCTION
A classic experiment in self-organization (first devised by Benard in 1900) is depicted in Figure 4. A viscous fluid is held between a uniform heat source below and the cooler temperature of the air above. That is, there is a potential difference with a field fbrce F of a magnitude determined by the difference between the two temperatures. When F is below a critical threshold heat flows from the source to the sink (entropy is produced) as a result of the disordered collisions between the constituent molecules (see Figure 4a); when F is increased beyond the critical threshold Bdnard "cells" emerge spontaneously, each cell consisting of hundreds of millions of molecules moving collectively together.
The major point to be emphasized here is that there is nothing improbable about the emergence of Benard cells; it is a completely lawful phenomenon. Each time F is increased beyond a critical threshold order emerges spontaneously. What is the critical threshold? It is simply the minimum magnitude of F that will support the ordered state. In other words, order production is entirely opportuni5tic: it occurs as soon as it gets the chance. The latter is understandable from the proposed law of maximum entropy production-systems will produce or select those dynamics that minimize their field potentials at the fastest possible rate given the constraints (Swenson, 1988, 1989b, 1989c, in press-b). Figure 5 shows the discontinuous increase in heat transfer that occurs with the production of the ordered state. Because the second law requires that entropy production increase concomitantly with the local entropy reduction of the ordered state, a phenomenon of the kind depicted in Figure 5 will be the case at whatever level order production occurs: Order is selected inexorably according to the law of maximum entropy production for precisely this reason.
|FIGURE 5 The discontinuous increase in the rate of heat transport effected by the disorder-to-order transition in a simple fluid experiment similar to that in Figure 4. The rate of heat transport in the disordered regime (Boltzmann regime) is given by V, and V + a is the heat transport in the ordered regime [3.1 x 10' H(cal x cm.-' x sec-')]. From "Engineering Initial Conditions in Self-Producing Environment" by R. Swenson, in M. Rogers and N. Warren (Eds.), A Delicate Balance: Technics, Culture and Consequences (p. 70), 1989d, Los Angeles: Institute of Electrical and Electronic Engineers (IEEE). Copyright 1989 by IEEE. Reprinted by permission. Data originally from Malkus (1954).
With the selection of order from disorder, a switch from the summative linear kinetics of the disordered regime to the autocatakinetics of the self-organizing state occurs and brings.with it a qualitatively different kind of behavior. The term autocatakinetics, which as Lotka (1945) noted was first used by Ostwald, has been reintroduced into the literature in an updated form as the minimal or most generalized description of a spontaneously ordered or self-organizing state (Swenson, in press-a, in press-b). An autocatakinetic system (Figure 6) maintains its "self" as a state constituted by, and empirically traceable to, a set of nonlinear (circularly causal) relations through the dissipation or breakdown of field potentials (or resources) in the continuous coordinated motion of its components (from auto-"self" + cata-"down" + kinetic, "of the motion of material bodies and the forces and energy associated therewith" from kinein, "to cause to move").
The generic dynamics of autocatakinetic systems, and of fields of autocatakinetic systems interacting together, is behaviorally rich. Autocatakinetic systems are self-amplifying sinks that opportunistically pull field potentials (resources) into their own self-production by extending the space-time dimensions of a field and thus its dissipative surfaces. The greater the dissipative space, the greater the per-unit-time coupling of sources and sinks (potentials and drains, respectively). This fact is readily seen in the Benard experiment. Whereas in the disordered regime (Figure 4a) the intrinsic units of space and time are of the order of 10 -8 cm and 10-5 g (the mean-free-path distances and relaxation times), in the ordered regime (Figure 4b) the intrinsic dimensions, as defined bythe coordinated motions of the components that constitute the cells, increased to centimeters and seconds. This extension of the dissipative space of the fluid by orders of magnitude accounts for the increase in the rate of entropy production seen in Figure 5.
|FIGURE 6. Figure shows generalized autocatakinetics where E' and Ell indicate a source and a sink with the difference between them constituting a field potential with a force F1, the magnitude of which is a measure of the difference. deltaEI is the autocatakinetic flow and deltaS the entropy production. EIII is the internal potential carried in the autocatakinetic relations, and F2 is the internal force produced by EIII that feeds back to amplify or maintain deltaEI. From "Emergent Attractors and the Law of Maximum Entropy Production: Foundations to a Theory of General Evolution" by R. Swenson, 1989b, Systems Research, 6, p. 191. Copyright 1989 by Pergamon. Adapted by permission
Autocatakinetic systems spontaneously select their own internal degrees of freedom so as to maximize the extension of their dissipative surfaces, which in the Benard experiment produces a time-independent state of regularly arrayed hexagonal cells (not shown). Because surface area increases as the square of a linear dimension whereas volume increases as the cube, isometrically growing autocatakinetic systems bifurcate spontaneously above some minimal size and proliferate their dissipative surfaces by fissioning. The point is, the ability of an autocatakinetic system to capture and transform energy resources is limited by its inputs and outputs, which are a function of its dissipative surfaces. Consequently, because its volume increases faster than its surface, as the system grows, it becomes increasingly less efficient at capturing and transforming energy. At some minimal threshold it becomes unstable to spontaneous division or fissioning by which surface-to-volume ratio is immediately increased.
Such fissioning is commonplace. It is observed in the Benard experiment, in the multiplication of living cells, and in the increase in population through the proliferation of villages during the Paleolithic period from approximately 1,500 villages at the beginning to about 75,000 villages at the end (Carneiro, 1987b; Swenson, in press-c). Under the constraint of entropy production maximization, surface-volume ratios play a fundamental level-independent role in determining the way things are (the symmetry states they assume). Prokaryotes, because they are diffusion limited, are an order of magnitude smaller than eukaryotic cells; and eukaryotes, because they needed an increased internal surface area to maintain their size, which required a membrane and an energy system dependent on atmospheric 02 above a minimal level, did not appear on earth for 2.5 billion years. Figure 2 tells the story of how form literally explodes into being (in geological time) as soon as the global chemical potential (the internal force in Figure 6) is of a sufficient magnitude to drive specific dissipation rates inhering in respiration and transport processes that could support the volume. The proposed selection principle provides a physical basis for Haldane's (Carneiro, 1987a) claim that evolution is a struggle to maximize surfaceto-volume ratios which can be seen as the expected behavior of the Earth system as a global self-organizing whole to maximize the extension of its dissipative surfaces over evolutionary time.
In summary, it is noted that each level, and each kind of material substrate, will present specific conditions for spontaneous ordering. The exact details of the conditions sponsoring order will have to be worked out for each particular instance-level-independent law acts on level-dependent substrates and the substrates themselves are emergent. At the same time, the process that engenders spontaneous ordering is expressible in a very general fashion, indifferent to the specifics (Figure 6). What the proposed law of maximum entropy production addresses is the bias obs7erved from instance to instance, namely, that systems progress in the direction of the most rapidly dissipative states given the conditions.
OPPORTUNISTIC THERMODYNAMIC ORIGINS OF
VISUALLY GUIDED ACTION
T'he physical account of evolution espoused here assumes that the Earth will evolve as a global entity so as to maximize the extension of its dissipative surfaces and to degrade, thereby, the geo-cosmic potential at the fastest possible rate given the constraints (Swenson, 1988, 1989a, 1989c). As intimated, this account has consequences for understanding the origins of the perceptual guidance of movements and the movement enhancement of opportunities to perceive. In this section and the next, the previous intimations are made explicit and the thermodynamic reasons for perception-action cycles are identified.
Another example of a thermodynamic field, similar to the glass of water in the room used earlier, is a warm mountain cabin sitting in cold, snow-covered woods. This field will spontaneously configure so as to dissipate (minimize) the temperature gradient or potential in whatever ways are possible. The opportunities include losing heat (producing energy flows) through the walls, through cracks in the walls, through the gap beneath the door, and through the window to the extent that it is open. In like manner, the geo-cosmic field can be expected to seize, in opportunistic fashion, accessible dimensions of dissipation as they are available. Examination of the solar absorption pattern for the planet shown in Figure 7, together with examination of the solar radiation spectrum for the planet shown in Figure 8, reveals a tremendous window of opportunity (in the very literal sense of an open window in the earlier warm cabin example) for producing thermodynamic flow with respect to the potential in the 0.4 to 0.7 nanometer range of the electromagnetic spectrum.
|FIGURE 7 The absorption spectrum of the atmosphere where I = total absorption and 0 = no absorption. From Environmental Systems (p. 47) by 1. White, D. Mottershead, and S. Harrison, 1984, London: Allen & Unwin. Copyright 1984 by Allen & Unwin. Reprinted by permission.
Opening the window in the heated cabin would produce a heat flux through the window. Consistent with the same physical principles, the window in the absorption spectrum (Figure 7) coupled with the massive solar emissivity in this range (more than half of the total; Figure 8), would be expected to produce a dissipative flux. Because the quantity of matter on Earth can be taken to be conserved (it has remained relatively constant since Hadean times) then such a flux-consistent with Vernadsky's (1929/1986) earlier view-must be through the progressive ordering (cycling) of the constituent biogeochemical components. Given the lawful nature of progressive ordering or level-building behavior, it is hardly surprising that the light distribution supporting perceptually guided actions, namely, the visible spectrum, is precisely in this same narrow range as Figure 9 reveals. Indeed Wachtershauser (1987) showed that it could not have been otherwise2.
As noted earlier, the first photosynthetic bacteria, by hooking the solar source to outgassed, reduced compounds such as hydrogen sulfide and sulfur, were able to transcend the limits on fermenting bacteria that were dependent on abiogenic organic compounds. Not much later in geological time, protocyanobacteria accomplished true photosynthesis, namely, oxygenic photosynthesis, by applying two photons to the cleavage of one water molecule. They linked the unlimited photon supply of the solar source to the unlimited supply of electrons in water, releasing oxygen into the atmosphere. The portion of the electromagnetic spectrum used for oxygenic photosynthesis is lawfully specified by the constraints of photocheriiistry. In particular, wavelengths higher than 700 nanometers are not strong enough to drive the reaction, and wavelengths below 400 nanometers chemically destroy the organic molecules, for example, proteins and DNA, entailed in the process. The mutuality of the photochemical laws and the potential of the solar window is readily appreciated: The facts of photochemistry afford the self-organization of autocatakinetic entities to drain the potential.
FIGURE 9 Visible wavelengths of the electromagnetic radiation spectrum.
The receptors for nonphotosynthetic bacteria were first used for detecting food. Similarly, photopigments were first used in photosynthesis, and in locating or moving toward or away from places where the wavelength of light was suitable or not suitable, respectively, for photochemistry (e.g., lower in the water where the visible spectrum is still strong but where the ultraviolet rays are no longer harmful). At some point, when cyanobacteria are presumed to have constituted a major portion of the biomass on earth, they themselves represented a field potential on which heterotrophs (which require carbohydrates both as an energy source and for biosynthesis) began to feed. The heterotrophs used the same photopigments for detecting light, but not to photosynthesize; instead the pigments were used to detect light that was specific to where the autotrophs (photosynthesizing cyanobacteria) were feeding (on the light). Light distributions specifying not light as food itself, but information about the location of food, was evolutionarily instantiated in its modern sense. Although the pigments making possible the registration of light distributions were derived from photosynthetic origins, they were not used for photosynthesis itself but for tracking down second-order photosynthetic potentials. The significance of the foregoing is that a higher order phenomenon (in this case, the autocatakinetics entailed by heterotrophic feeding off the cyanobacteria), constrained by a higher order description of light (not light as such, but what it specifies), increases the intensity of the thermodynamic flow. It provides an additional means of hastening the degradation of the geo-cosmic potential. Contemporary nonphotosynthesizers (e.g., ourselves) contribute to that hastening in a manner that is evolutionarily continuous with that of the heterotrophs: Maintaining the capacity to see requires vitamins, such as vitamin A, which must be obtained by consuming plants and/or bacteria.
2. It is not our intention here to endorse every detail of Wachtershauser's scheme. A deeper discussion is beyond the scope of this article, but his central argument, which is well demonstrated does not depend on those details.