Swenson: Advances in Human Ecology, Vol. 6, 1997

Symmetry and Broken Symmetry Again:
The Classical Statements of the First and Second Laws of Thermodynamics

The insistence of Heraclitus on the importance of persistence and change, and his view of the world as an ongoing process of flow, would certainly seem to qualify him as the foremost ancient progenitor of what would become the science of thermodynamics. Leibniz's assertion that there must be something that changes and something that remains the same, or something conserved, and his very aggressive work to identify the conserved, and active quantities of the world, certainly qualify him as the modern founder of thermodynamics. The work of Mayr, and also Helmoholtz, who are credited, among others with formulating the first law can be traced in a direct lineage to Leibniz. One may also locate legitimate roots for the laws of thermodynamics in those who searched for symmetry principles, Parmenides among them, because the first and second laws, understood in the deepest sense, are symmetry principles. Eddington (1929) has argued that the second law holds the supreme position among all the laws of nature, but, it is probably more accurate to say that the first and second laws together hold the supreme positions among all the laws of nature, because they are each dependent in a certain way upon the other.
Following the earlier work of Davy and Rumford, the first law was first formulated by Mayer, then Joule, and later Helmoholtz in the first half of the nineteenth century with various demonstrations of the equivalence of heat and other forms of energy. The law was completed in this century with Einstein's demonstration that matter is also a form of energy. With its recognition that all natural processes can be understood as flows or transformations of different forms of energy, and that the total quantity of energy always remains the same, or is conserved, the first law provided the basis for unifying all natural processes through the recognition of their underlying time-translation symmetry. The first law, in other words, expresses what remains the same through all natural processes, regardless which way one goes in time. This presumably would have made Parmenides happy because as far as the first law goes nothing, in effect, changes, or, in other words, there is no time. When the potential energy of an elevated body of water is, by its fall, turned into mechanical energy to drive a mill wheel, and the mechanical energy, in turn, is dissipated into the surrounds as heat from the friction of the millstone, the total amount of energy is conserved, or has remain unchanged, and that is what the first law says ("energy is never created or destroyed" is thus another statement of the first law).
Until Clausius and Thomson (later "Lord Kelvin") came along there was nevertheless some confusion and doubt about this law. This was because, as Joule's experiment (Figure 6)
demonstrating the conservation of energy

Figure 6. Experiment devised by Joule to show the conservation of energy. When a constraint is is removed potential energy in the form of a suspended weight is converted into the mechanical or kinetic energy of a moving paddle wheel in an energy-tight container of water heating the water by an amount consistent with the amount of potential energy lost by the falling weight.

unintentionally showed, for example, there is a broken symmetry to natural processes, a one-way flow of things that, in contrast to the first law, establishes the notion of time, that there is a difference between the past, present, and future. The same is easily seen with the example of the mill wheel.
It was the relation between the symmetry on the one hand, and broken-symmetry on the other that Clausius and Thomson showed with their formulation of the second law in the 1850's. It was the work of Carnot, some twenty-five years earlier, that brought the problem to a head. Carnot had observed that like the fall of a stream that turns a mill wheel, it was the "fall" of heat from higher to lower temperatures that motivated a steam engine. That this work showed an irreversible destruction of "motive force" or potential for producing change suggested to Clausius and Thomson that if the first law was true then energy, contrary to popular misconception, could not be the motive force for change. Recognizing in this way that the active principle and the conserved quantity could not be the same they realized that there must be a second law involved. Clausius coined the word "entropy" to refer to the dissipated potential, and the second law states that all natural processes proceed so as to maximize the entropy (or equivalently minimize or dissipate the potential), while energy, at the same time is entirely conserved. The balance equation of the second law, expressed as says that in all real world processes entropy always increases,.
The active nature of the second law is intuitively easy to grasp and empirically easy to demonstrate. Figure 7 shows a glass of hot liquid placed in a room at a cooler temperature. The difference in temperatures in the

Figure 7. A glass of liquid at temperature TI is placed in a room at temperature TII such that . The disequilibrium produces a field potential that results in a flow of energy in the form of heat from the glass to the room so as to drain the potential until it is minimized (the entropy is maximized) at which time thermodynamic equilibrium is reached and all flows stop. refers to the conservation of energy in that the flow from the glass equals the flow of heat into the room. From "End Directed Physics and Evolutionary Ordering: Obviating the Problem of the Population of One" by R. Swenson, in F. Geyer (Ed.), The Cybernetics of Complex Systems: Self-Organization, Evolution, and Social Change, p. 45, 1991, Salinas, CA: Intersystems Publications. Copyright 1991 Intersystems Publications. Adapted by permission.

glass-room system constitutes a potential and a flow of energy in the form of heat, a "drain" on the potential, is produced from the glass (source) to the room (sink) until the potential is minimized (the entropy is maximized) and the liquid and the room are at the same temperature. At this point, all flows and thus all entropy production stops and the system is at thermodynamic equilibrium. The same principle applies to any system where any form of energy is out of equilibrium with its surrounds (e.g., mechanical, chemical, electrical, or energy in the form of heat), a potential exists that the world acts spontaneously to minimize.

The Second Law as a Law of Disorder

The active macroscopic nature of the second law presented a direct challenge to the "dead" mechanical world view which Boltzmann tried to meet by reducing it to a law of probability following from the random collisions of mechanical particles. Following Maxwell, and modeling gas molecules as colliding billiard balls in a box, Boltzmann noted that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder‹the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder‹the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium‹or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction," Boltzmann (1886/1974, p. 20) concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."
Boltzmann himself acknowledged that his hypothesis of the second law had only been demonstrated for the case of a gas in a box near equilibrium, but the science of his time (and up until quite recently) was dominated by linear, near-equilibrium or equilibrium thinking, and this view of the second law, as a law of disorder, became widely accepted. The world, however, is not a linear, near equilibrium system like a gas in a box, but instead nonlinear and far-from-equilibrium, and the second law is not reducible to a stochastic collision function. As the next subsection section outlines, rather than being infinitely improbable, we now can see that spontaneous ordering is the expected consequence of natural law.

Why the World is in the Order-Production Business

The idea that living things violate the second law of thermodynamics was temporarily deflected in the middle of this century when Bertalanffy (e.g., 1952, p. 145) showed that "spontaneous order...can appear in [open] systems" (systems with energy flows running through them) by virtue of their ability to build their order by dissipating potentials in their environments. As briefly noted above, along the same lines, pointing to the balance equation of the second law, Schröedinger (1945) popularized the idea of living things a streams of order which like flames are permitted to exist away from equilibrium because they feed on "negentropy" (potentials) in their environments, and these ideas were further popularized by Prigogine (e.g., 1978).
Schrödinger's important point was that as long as living things like flames (and all autocatakinetic systems) produce entropy (or minimize potentials) at a sufficient rate to compensate for their own internal ordering or entropy reduction (their ordered departure and persistence away from equilibrium), then the balance equation of the second law, which simply says that entropy must increase in all natural processes, would not be violated. According to the Bertalanffy-Schröedinger-Prigogine view, order can arise spontaneously, and living things are thus permitted to exist, as it became popular to say, as long as they "pay their entropy debt." While this made an important contribution to the discourse, and worked for the classical statement of the second law per Clausius and Thomson, on Boltzmann's view such "debt payers" were still infinitely improbable. Living things were still infinitely improbable states struggling, or fighting, against the laws of physics. The urgency towards existence captured in the fecundity principle and the intentional dynamics it entails, as well as planetary evolution as a whole were still entirely anomalous on this view with respect to universal law. What is more, as the Bénard experiment shows, simple physical systems also falsify the Boltzmann hypothesis. Order is seen to arise, not infinitely improbably, but with a probability of one, that is, whenever, and as soon as it gets the chance. The nomological basis for this opportunistic ordering was still a mystery, a point emphasized by Bertalanffy himself, who suspected there might be another thermodynamic principle that would account for this "build-upism", or, in the terms we have been using, the river that flows uphill.

Space-Time Relations, Order Production, and a Return to the Balance Equation of the Second Law

There are two key pieces to solving the puzzle or problem of the two incommensurable rivers. The first is discovered by a return to the balance equation of the second law. As discussed above, and illustrated in Figure 5, transformations from disorder to order dramatically increase the space-time dimensions of a system. What Bertalanffy and Schröedinger emphasized was that as long as an autocatakinetic system produces entropy fast enough to compensate for its development and maintenance away from equilibrium (its own internal entropy reduction or increase in space-time dimensions), it is permitted to exist. Ordered flow, in other words, to come into being or exist must function to increase the rate of entropy production of the system plus environment at a sufficient rate‹must pull in sufficient resources and dissipate them‹to satisfy the balance equation of the second law. This makes an important point implicitly, that was not specifically noted by Bertalanffy or Schroedinger, that will now be stated explicitly: Ordered flow must be more efficient at dissipating potentials than disordered flow (Figure 5 shows exactly how this works in a simple physical system). Figure 8 which shows the dramatic increase in the rate of heat transport from source to sink that occurs in the transformation

increased entropy production in spontaneous disorder to order transition

Figure 8. The discontinuous increase in the rate of heat transport that follows from the disorder-to-order transition in a simple fluid experiment similar to that shown in Figure 4. The rate of heat transport in the disordered regime is given by , and is the heat transport in the ordered regime [3.1 x 10 4H(cal x cm.-2 x sec-1)]. From "Engineering Initial Conditions in a Self-Producing Environment" by R. Swenson, in M. Rogers and N. Warren (Eds.), A Delicate Balance: Technics, Culture and Consequences (p. 70), 1989a, Los Angeles: Institute of Electrical and Electronic Engineers (IEEE). Copyright 1989 IEEE. Reprinted by permission.

from the disordered to ordered state bears this out, and given the balance equation of the second law, it could not be otherwise. This important point brings us to the second and final piece of the puzzle.

The Law of Maximum Entropy Production

The crucial final piece to the puzzle of the two rivers, the piece that provides the nomological basis for dissolving the postulates of incommensurability, is the answer to a question that classical thermodynamics never asked. The classical statement of the second law says that entropy will be maximized, or potentials minimized, but it does not ask or answer the question of which out of available paths a system will take to accomplish this end. The answer to the question is that the system will select the path, or assembly of paths, out of otherwise available paths, that minimize the potential or maximize the entropy at the fastest rate given the constraints. This is a statement of the law of maximum entropy production the physical principle that provides the nomological basis, as will be seen below, for why the world is in the order production business (Swenson, 1988, 1991, 1992, 1996; Swenson & Turvey, 1991). Note that the law of maximum entropy production is in addition to the second law. The second law says only that entropy is maximized while the law of maximum entropy production says it is maximized (potentials minimized) at the fastest rate given the constraints. These are two separate laws because the second, in principle, could be falsified without changing the first. Like the active nature of the second law, however, the law of maximum entropy production is intuitively easy to grasp and empirically demonstrate.
Consider the example of the warm mountain cabin sitting in cold, snow-covered woods (Swenson & Turvey, 1991). The difference in temperature between the cabin and the woods constitutes a potential and the cabin-woods system as a consequence will produce flows of energy as heat from the cabin to the woods so as to minimize the potential. Initially, supposing the house is tight, the heat will be flowing to the outside primarily by conduction through the walls. Now imagine opening a window or a door, and thus removing a constraint on the rate of dissipation. What we know intuitively, and can confirm by experiment, is that whenever a constraint is removed and a new path or drain is provided that increases the rate at which the potential is minimized the system will seize the opportunity. Furthermore, since the opened window, for example, will not instantaneously drain all the potential some will still be allocated to conduction through the walls. Each path will drain all that it can, the fastest (in this case the open window) procuring the greatest amount with what is left going to the slower paths (in this case conduction through the walls). In other words, regardless the specific conditions, or the number of paths or drains, the system will automatically select the assembly of paths from among those otherwise available so as to get the system to the final state, to minimize or drain the potential, at the fastest rate given the constraints. This is the essence of the law of maximum entropy production. Now what does this have to do with spontaneous ordering, with the filling of dimensions of space-time?
Given the preceding, the reader may have already leaped to the correct conclusion. If the world selects those dynamics that minimize potentials at the fastest rate given the constraints (the law of maximum entropy production), and if ordered flow is more efficient at reducing potentials than disordered flow (derivation from the balance equation of the second law), then the world can be expected to produce order whenever it gets the chancethe world is in the order-production business because ordered flow produces entropy faster than disordered flow (Swenson, 1988, 1991, 1992, 1996; Swenson & Turvey, 1991). Contrary to the older Boltzmann view where the production of order is seen as infinitely improbable, given this new understanding the world can be expected to produce as much order as it can, to expand space-time dimensions whenever the opportunity arises. Autocatakinetic systems, in other words, are self-amplifying sinks that by pulling potentials or resources into their own development and persistence away from equilibrium extend the space-time dimensions of the fields (system plus environment) from which they emerge and thereby increase the dissipative rate. The law of maximum entropy production, when coupled with the balance equation of the second law, provides the nomological basis for dissolving the postulates of incommensurability, and unifying living things with their environments‹for unifying the two otherwise apparently incommensurable rivers that flow up and downhill respectively. Rather than an incommensurable, inexplicable, and infinitely improbable anomaly, the river that flows uphill, the active ordering that characterizes terrestrial evolution of which biological, and cultural evolution are parts, is seen to be an expected manifestation of universal law.