Translation of physics articles by Soodak and Iberall in our reader Chapter 3 (Chs. 24 and 27 in Yates' Self-Organizing Systems.Ý It is expected that neither of these chapters will make any sense to you without this introduction.)

Thermodynamic Principles for the Social Sciences: An introduction to self-organizing systems

Douglas R. White

The physical sciences have already solved many of the problems of understanding the principles of self organizing systems.Ý Thermodynamics and the principles of self-organization, however, are the most difficult concepts to understand in this course, but also the deepest, the most rewarding, the most useful, and the most practical for social science research once they are understood.Ý It will be especially valuable to your work in "conceptualizing the social dynamics" of the system you choose for your term project if you can find one or more applications for these concepts.Ý

Why do I care about these articles in particular?Ý

Because if you follow a complex-systems strategy (elaborated by these authors) then the basic experimental procedures used in the sciences are no different in principle than those for the social sciences, and the underlying physical laws that govern all systems can be translated into theoretical and explanatory frameworks for the social sciences, subject to experimental verification.Ý One thing we will pay attention to is how to give a physical description of something not in terms of its attributes but its processes.Ý Typically, processes occur as a function of gradients from point to point in some field, where interaction leads to the equipartition of energies.Ý For example:Ý a moving billiard ball hits a stationary one and the combined momentum is equipartitioned, the moving ball becoming slower, the stationary one absorbs part of its momentum (total momentum is conserved, minus friction).Ý But unlike billiards, in a complex system the process description must include the internal processes of the actors.

For the readings in week 3, here is what I want you to know from ñ and as a background to ñÝ the first article. I will continue later with the second. [As always in this class, focus on the concepts and not on symbols or equations].

Some basic scientific foundations, and research strategies

It is useful to see how physics and chemistry approach their subject matters through definitions, experiments, and descriptions (dynamically: where do the driving energies and materials for observed processes come from?) concerning atomistic units and processes, e.g., beginning with the basics for simple systems:

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --

Thermodynamics (thermo=energy, dynamics=change): the study of the patterns of energy change.

Some important physical strategies and assumptions, from our perspective, are given below. We may think of them most easily in terms of a "games and simulations" approach:

The thermodynamics game: set up some boundaries around a "system" that separate "system" from its surroundings, with the following definitions

… isolated system = no exchange of matter or energy with surroundings

… closed system = no exchange of matter but some exchange of energy

… open system = exchange of matter and energy with surroundings

Experimental evidence shows that everything is composed of energy, either in pure form (e.g., big bang, an explosion of energy), or condensed into structures (atomisms E=mc²).Ý

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --

First law of Thermodynamics: the sum total of the energy in a system and its surroundings, over time, is constant (Conservation Law).

If we consider an atomism as a system that is difficult to break apart (an experimental observation: equally applicable to social groups and social bonds), there is energy in the bonding of atomic constitutions that has to come out of the environment, and when that bonding is broken that energy is released.

Dfn. Forms of energy, e.g.: Heat (q)=exchange of thermal energy (stored as kinetic energy of atomisms, i.e., movement, where the "heated" or diffusive movements of atomisms are uncorrelated, net undirected)=the capacity to diffuse kinetic movement via collisions from "hot" bodies to "cold" bodies in a unit of time; Work(w)=net directed (convective) movement of matter from one location to another = external force x distance moved.

Note that work requires an external force (and thus energy from the surrounding environment).Ý Heat, on the other hand, tends to equipartition thermal energy via diffusive collision and thus tends to thermal equilibrium: within a system at equilibrium there are no further gradients to do useful work (see second law).

Dfn. Thermodynamic engine: A (nonisolated) system where energy is transferred from the surroundings to do work.Ý E.g., when a piston is moved by heating gas in a chamber, the work done is PV (pressure x volume).

The energy in a thermodynamic engine is sometimes described by its enthalpy H= E +PV where -PV is the work done and +PV is the correction for energy used in doing work on the surroundings.Ý H is the capacity of energy differentials to diffuse heat (relative to a surrounding) or to do work.Ý (Because thermodynamic engine processes are often cyclical, and depend on discrete quanta of energy per cycle, H may be quantized).

Energy and enthalpy are state variables of a system.Ý If heat and work are the only forms of energy transferred between a system and its surroundings in a closed system, then the first law states for enthalpy: E2-E1 = Dheat + Dwork = q + w, where D is the symbol for change in a quantity.

Chemistry involves the study of bond energies (enthalpies) that are released when a bond is are broken and consumed when a bond is made (changes of state).Ý For chemical transformations at a constant (e.g., atmospheric) pressure, the change in enthalpy will be q; typically, some quantum of energy.

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --

Thermodynamic (Carnot-Clausius) Entropy (S @ -w). The quantitative measure of thermal energy not available to do work (the opposite of w, the energy available to do work).Ý Clausius noticed a certain ratio that was constant in reversible (ideal) heat cycles studied by Carnot, and in 1865 named this ratio "entropy" after deciding that it must correspond to a real physical quantity.

Second law of Thermodynamics: The sum of energy available for work in a system and its surroundings never increases (an experimental finding for all known systems).Ý Corollaries: (1)Ý the energy available for work in an isolated system never increases spontaneously; (2) entropy is not conserved, and can only increase in an isolated system; (3) the sum of entropy in a system and in its surroundings can only increase over time; (4) a system can lose entropy (become more capable of doing work through directed gradients) only at the expense of greater entropy in its surroundings, as a function of net energy flows from the surroundings that provide gradients to do useful work within the system.

[See http://www.cchem.berkeley.edu/~chem130a/sauer/outline/secondlaw.html#carnot

from the previous menu for an example of the 4 cycles of the operation of a piston in a carnot heat engine]

Configurational (Boltzmann-Gibbs) Entropy (S). A measure of disorder or randomness in a closed system.Ý Boltzmann resolved the apparent contradiction between gas laws at the molecular level, where an elastic collision between molecules would look the same going forward or backward in time, and the second law, which seems to imply irreversibility at the macrolevel. Processes that occur within a sufficiently short time so that entropy is constant are reversible.Ý His model of how heat is evenly diffused through a gas also showed for the mixing of two gasses that the same processes would lead to thorough mixing.Ý This led Boltzmann to define the "disorder" of a system, such as a solid, liquid or gas, as "the number of ways [W] that the insides can be arranged, so that from the outside it looks the same.Ý The logarithm of that number [ln W] of ways is the entropy" (Feynmann 1963 vol. 3 section 46-5).Ý There are no physical units for this kind of entropy, but Boltzmann defined a constant k for gasses, experimentally determined, that relates absolute temperature to the average kinetic energy of a molecule -- a universal constant -- so as to define configurational entropy as:

S = k ln W.

Since k is constant for all molecules, if we know thermodynamic entropy S, then Boltzmann's equation can be used to solve for W, the number of microstates to which a system can transform in a given phase or state, and checked experimentally. Thermodynamic entropy and configurational entropy can be equated for physical domains without violating any known physical laws or results of experiments.

Example: S(ice) < S(water) < S(gas); there are fewer ways for the molecules in a solid or crystal to rearrange themselves by their internal movements than for a fluid, and fewer for a fluid than for a gas. Ice is said to be more highly ordered that water or water vapor.Ý (The Third law of Thermodynamics is that the entropy of all pure perfect crystals is zero at absolute zero temperature).

Extension of the Second law. Configurational entropy in a system and its surroundings never decreases. A corollary is that a system can lose configurational entropy (become more ordered or organized, etc.) but only by an increase of configurational entropy in its surroundings.

Logical (Shannon) Entropy (S*).Ý Claude Shannon used the term entropy to refer to disorder in information.Ý The problem, however, would be to determine: What are the number alternative arrangements of elements that constituted a chunk of "information" while "it still looks the same from the outside"?Ý While it would seem that a "second law" should apply to information -- in that nothing ever orders or organizes itself without an input of energy -- there is no equivalent of Boltzmann's constant, no way to measure W directly, and no clear experimental results on necessary "energetic inputs" required to organize information (but see the PhD thesis of David Richard Wolf, Physics, University of Texas, Austin). WolfísÝ Information and correlation in statistical mechanical systems introduces higher order information measures based on the discovery by E. T. Jaynes (1957 Principle of Maximal Entropy) of elegant connections between statistical mechanics and the entropy introduced by Shannon:

ÝÝÝÝÝ "In this dissertation the question of how information is carried in a physical system is examined. The systems studied here

ÝÝÝÝÝ are simple, as are all systems which have a presentable analysis. The point of view that the states of the physical system of

ÝÝÝÝÝ interest may be treated probabilistically, that there is an underlying distribution which describes the probability that a

ÝÝÝÝÝ particular state occurs, is taken thoroughly. Certainly the thermodynamic systems studied here are treated on this basis, but more generally whenever such a distribution exists and is known, or is learnable, the methods of this work apply."

For the same reasons that most scientists regard Shannon entropy as ill-defined, Darwin and Darwinian evolutionists are wary of defining some species as more evolved, more organized, or more complex (Gould 1995, Dawkins 1995, Maynard Smith and Szathm·ry 1995).ÝÝ Does their wariness imply that all organisms equally highly evolved (Margulis and Sagan 1995:44)?Ý In what follows, I consider Soodak and Iberall's answer to this question.

A system that is at (thermal) equilibrium internally and with its surrounding is incapable of doing work, since there exist no gradients to external forces to operate.Ý Any system that is not at thermal equilibrium has organized gradients of energy, and these gradients necessarily depend on energy inputs from its surroundings.Ý

Hence systems can be stacked, as shown in Figure 1: system S1 exchanges energy with its "surround" S2, and system S2 exchanges energy with its "surround" S3.Ý The universe is full of embedded systems, like Chinese dolls.

ÝÝÝÝÝÝ

example:Ý S3 solar system, S2 earth system, S1 life system

Figure 1: Embedded Systems

We now have enough conceptual scaffolding to start to "translate" what Soodak and Iberall (1978) are saying about thermodynamics:Ý From bondings at the subatomic to atomic to molecular to organized matter to cells, organs, species, polities, etc., a hierarchical stacking of systems into levels is organizationally consistent with the 2nd law.Ý In embedded or stacked thermodynamic systems (as illustrated in Figure 1), as the "outer" more macroscopic systems dissipate, they release thermal energy (no longer capable of doing work at that level) that represents rising entropy at that level but which at more micro levels within that system can be converted into organized thermodynamic gradients that can be harnessed (by generalized Darwinian selection) into engine processes (once an engine process begins, it is possible that it will replicate itself for a longer time period of Darwinian "survival").Ý That is the key to understanding evolution.Ý All kinds of embedded systems evolve, living and nonliving.Ý Life is a special case of ìself-organizingî system where it is thermodynamic stacking that is doing the organization.

Thus, the energy available to do work in a system (and the organization of a system, if we knew how to measure it properly) can increase, not in contradistinction to the second law, but only because energy is flowing into the system from its surround. For example: energy is dissipated from the sun as light that creates energy gradients available to do work on earth. This is key to understanding organization generally, to understand human society and culture, and to understanding how to develop an experiment-and-observationÝ based social science that is scientifically grounded.

Ch. 24. Soodak and Iberall.Ý Thermodynamics and Complex Systems - a reading guided by thermodynamic principles given above.

It is the organization (organized gradients) of energy and matter differentials that determines what gets done within a system: "process is guided and constrained by structure; structure is laid down, maintained, changed, and degraded by process." pp. 459-460.

Hence the energy flows and time scales follow such sequences as:

energy release in a big bang -> creates

ÝÝ windup of galaxies -> condense to create

ÝÝÝÝÝ explosion of stars -> convert

ÝÝÝÝÝÝÝÝ hydrogen into more complex molecules = that form

ÝÝÝÝÝÝÝÝÝÝ more diverse forms of matter -> condense into

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝ planetary systems -> support

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ planetary geochemistries -> support

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ origins of diverse forms of life -> which serve as

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ platforms for more complex forms of life -> that form

ÝÝÝÝÝÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝall kinds of associations -> etc.

Microlevel kinetics, what can move where and interact with what in different states (e.g., ice/water/vapor), is what giver rise empirically to the entropy of a field, and to the dynamic behavior of a field of interacting atomisms.Ý pp. 460-461:Ý "macroscopic coordinates and their interactions... are emergent properties, arising from the kinetic behavior; and they represent ... constraints on the kinetic behavior. Thus the micro- and macro-levels are mutually linked."Ý The macrobehavior of the field, in turn, "is constrained by boundary conditions from outside the system ... [which] often originate from a higher-level system of which the macroscopic system is simply one of the atomistic units."

The following three topics can be fleshed out by reading Soodak and Iberall:

time scales of internal processes - factory day cycle of repeated processes p. 461

[thermodynamic engine processes must be cycled, with energetic ìkicksî from the environment, to operate near-equilibrium at various time scales for a system to survive]

measure of complexity = ratio of internal/external process time 461

[Note that by this criteria increases in complexity are not a necessary outcome of evolution but may be identified empirically when they do occur if we have sufficient knowledge of dynamics.]

cascade spectrum = 462

"Complex systems tend to display a cascade spectrum of many relaxation processes [thermodynamic engine processes driven by external energetic inputs and internal dissipation of gradient energies towards equilibrium interrrupeted by new external en ergetic inputs].

Structure Formation

The central task of the social sciences is to understand the structures and processes that are constituitive of society, polity, economics, culture -- of human life in general.Ý The great contribution of systems physics as developed by Soodak and Iberall (following standard physics applied to stacked or hierarchical systems as actually observed in our universe) is to understand how "structure is laid down, maintained, changed, and degraded by process" and conversely " process is guided and constrained by structure."Ý In physical systems, structural changes at a micro level (addition of elements or actors, interactions, energetic inputs, changes in velocities, etc.) are defined as incremental if they lead to no changes in macrobehavior, and as phase transitions when they lead to discontinuous macrobehavioral change, such as the major change in entropy between a solid and a liquid state.Ý The contribution of Soodak and Iberall, specifically, is a scientific theory of phase transitions that they develop as a generalization of the physical theory of flow dynamics (energy and material flows).Ý

They begin with the phase transitions predicted by the Reynolds number for flow processes in fluids, in which, like any physical process, there only three possible ways for energy or materials to move:

… by the kinetic energy (local movement) of molecules or atomisms, the energy of motion (called diffusion or Brownian motion) is transmitted by collision. As Einstein demonstrated, molecules that move and collide randomly will move away from their origin, but only on average as a function of the square-root of time [see http://www.ms.uky.edu/~mai/java/stat/brmo.html and http://www.stat.umn.edu/~charlie/Stoch/brown.html on the previous menu to see examples of Brownian motion].Ý

… by directed movements at a constant inertial velocity (called convection) of coherent ensembles of molecules or atomisms.Ý In directed movement at a constant velocity, by definition, molecule or atomisms move a distance proportional to (a linear function of) time.

… by omnidirectional vibration (called wave propagation). Atomisms (e.g., light, sound) will move on average a distance that is also a linear function of time.

There are, in nature, no known means of motion other than diffusion (movement following random interactions and equipartition of energy and momentum), convection (movement following gradients) and wave propagation (vibratory movement characterizing light, sound, gravity).

It is experimentally observable in physical systems that for a kinetic system at equilibrium, in which motion occurs by diffusion (random movements into available degrees of freedom), relatively small energy (e.g., thermal) gradients will not produce convection but only an increased rate of diffusive motion.Ý The Reynolds number of a fluid system is a ratio, in standardized units, of an observed external gradient (acting on a system from its surrounding, e.g., heat incoming from some point on the system's boundary), to the capacity of the system atomisms to absorb such energies and transmit or dissipate them locally by increased random (Brownian) motion that, through local collisions, will diffuse these energies onmidirectionally (as a function of the square-root of time) throughout the system.Ý When Reynolds ratio reaches 1, this capacity to absorb energy kinetically is exhausted, and convection appears to transport energy in a directed fashion away from those parts of the system boundary where the gradient appears.Ý The convection may be irregular, in the form of turbulent eddies, and is governed by the Navier-Stokes equations, which are non-linear, difficult or impossible to solve without approximations, and hence somewhat unpredictable (like the weather).Ý For an external energy gradient of a certain magnitude at the boundary of a system, Reynolds number can be expressed as the ratio of the time needed to diffuse the gradient a distance L_o (on the order of L_o² r/m, where rho or r is the density of the atomism, and tau or t is the time between random collisions of the atomisms) relative to the time needed to convect the gradient a distance L_o (on the order of L_o/V, where V is the velocity of the incoming flow). Hence,

ÝÝÝÝ Re = (L_o² r/m) / (L_o/V) = L_oVr/m

ÝÝÝÝÝÝÝÝÝÝ = time to diffuse a distance L_o / time to convect a distance L_o

ÝÝÝÝÝÝÝÝÝÝ = Velocity V (convection) / Velocity v (diffusion) = (L_oV) /(m/r)

ÝÝÝÝÝÝ < 1 diffusion time can handle convective flow, no structural change

ÝÝÝÝÝÝ = 1 transition from microscopic transport to macroscopic transport

ÝÝÝÝÝÝ > 1 when diffusion time too short to handle convection, structural change

ÝÝÝÝÝÝ and when >> 1, turbulence begins in fluids

pp. 462-464

To see the effects of variables V, L_o, rho, c, tau and mu on the emergence of macrostructure in fluid processes, we can look at the direction of each effect on the emergence of associations of sets of atomisms that will diffuse as a unit once the Reynolds threshold of phase transition is passed.Ý Each of the variables has effects on clumps of atomisms sticking together and moving as a unit in response to incoming flows of energy or materials, in this case in a fluid system, as shown below:

VARIABLE having an effect on a ...ÝÝÝÝÝÝÝÝÝÝÝÝÝ Higher likelihood of transition if ...

V=velocity of some incoming flowÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ...more stress on a system with..

v=velocity of diffusionÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Öslower diffusive velocity withÖ

t(tau)= average time between collisionsÝÝÝÝÝÝÝ ...less time between collisions,

vt=diffusive movement in time unit tÝÝÝÝÝÝÝÝÝÝÝÝ Öless distance between collisions,

L_o=diameter of atomistic cellsÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ...bigger atomisms that areÖ

r(rho)=density of the atomism or networkÝÝÝÝ ...more dense, withÖ

c= speed of propagation through fluid, netwk ...less propagative dissapation,

ÝÝÝ (via sound vibration), andÖ

m(mu)=shear viscocity = r t c²ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ...less sticky with one another.

ÝÝÝ (transport: more dense, slower collisions, more propagative-gel-solid-like)

Reynolds equations also predict the number and size of the fluid cells or organizational units that emerge in the macrostructure of diffusive flows following phase transition.Ý For stability at a Reynolds transition, the number N of higher order cells or atomisms that emerge, and their diameter D on a surface are:

ÝÝÝÝ N > (vt/VL_o)²

ÝÝÝÝ D = L_o / ÷N

Iberall and Soodak's (1978) claim is that phase transitions in all systems -- the emergence of structure out of dynamics -- are governed by Reynolds laws (where transitions are called departures from dynamic similarity), and that this can be confirmed by observation.Ý

Highly coordinated states are not irreversible but depend for stability on dynamic throughputs. As more energy is added to a system, transitions to more coordinated states do not imply greater freedom at lower atomistic levels in the systems-hierarchy, such as at the level of individuals in population systems, but greater coordination of trajectories in convective-cell movement.Ý

The first row of Table 1 shows stability transition calculations used by Iberall and Soodak (1978:18) to compute constellations of superatomisms ñ the proto-urban agricultural settlements engaged in trade ñ emergent in the post-Neolithic. The expression L_oV/vt is the ratio of normalized convective trade velocity to normalized viscous relaxation velocity, which when multiplied by ÷N, where N is the number of convective superatomisms, cannot fall below a Reynolds number Re > 1 by conservation law.Ý Here, the minimum number of interacting centers is Nª16.Ý Row 2 of the table repeats these computations for a hypothetical transition to animal husbandry, with larger cell diameters (size of territory occupied) and higher viscous velocity.ÝÝ

Table 1: Stability Transitions	generational relaxation time t (days)	cell diameter Lo (miles)	convective velocityÝ V (miles/day) [trade, husb.]	viscous velocity v (miles/day)	Re > 1ÝÝ _ ÝÝÝÝÝÝÝÝ =÷N(VLo/vt) \ NÝÝ >ÝÝÝ (vt/LoV)^2	minimun number of superatomisms N ª
Protourban Trade	7000	40	5/1	40/365	(40x7000/365x5x40)^2	16
Animal Husbandry	7000	200	5/1	120/365	(200x7000/365x5x120)^2	Ý 9

In Yates Ch. 27 Iberall and Soodak (1987) illustrate phase transitions in fluid flow (pp. 503-504), matter condensation (pp. 507-508), chemical patterns (pp. 507-508) and social patterns such as the transition to urban nucleation (p. 508).

The transition from a reputational system for enforcement of honest behavior among European traders in the early Medieval period, to a system of judges (in the absence of centralized state system with police power and authority over a sufficiently wide geographical range to enforce commercial contracts), modeled by Milgrom, North and Weingast (1990), is an excellent candidate for modeling a Reynolds phase transition.Ý ìThe role of the judges, far from being substitutes for the reputation mechanism, [was] to make the reputation system more effective as a means of promoting honest trade.îÝ As trade intensified, ìin a large communityÖ it would be too costly to keep everyone informed about what transpires in all trading relations, as a simple reputation system might require.îÝ ìIntuitively, the system of private judges accomplishes its objectives by bunding the services which are valuable to the community, so that a trader pursuing his individual interest serves the communityís interest as wellî (p. 3).Ý Those are exactly the kinds of dynamical processes we expect in a Reynolds phase transition.Ý Question: is the spatial scaling and number of ìinitialî emergent units predicted by the Reynolds transition?

Another great application is the Reynolds type transition in scale and scope of modern industrial capitalism described in Chandler (1990), Chapter 1. Question: is the spatial scaling and number of ìinitialî emergent units predicted by the Reynolds transition?

How structure is stabilizedÝ p. 465

Two additional conditions for an emergent structure to form a stable association: (1) rapid transformation of binding energy, eliminated from the structure (given off as energy; energy must be put in to loosen the bonds), and (2) binding energy must be large compared to the energy of interaction between the structure and external agents (i.e., cannot be easily broken apart as incoming energy loosening bonds).

pp. 467- Extension to Society

[this section summarizes the thermodynamic approach to the study of society but does not return to examples of phase transitions, which is left to Ch. 27.Ý You can see if there are any parts of Ch. 27 that now make sense to you.Ý It is still tough going.]

References

Ch. 24. Soodak, H., Iberall, A. Thermodynamics and complex systems. Pp. 459-469 F.E.Yates, Ed. 1987. Self-Organizing Systems: The Emergence of Order. New York: Plenum.

Ch. 27. Iberall, A., Soodak, H. A physics for complex systems. Pp. 499-520. F.E.Yates, Ed. 1987. Self-Organizing Systems: The Emergence of Order. New York: Plenum.

Chandler, Alfred D. Jr., 1990. Chapter 1, The Modern Industrial Entreprise. Scale and Scope: The Ddynamics of Industrial Capitalism. Cambridge, Mass.: Belknap Press of Harvard University Press.

Iberall, A., Soodak, 1978. Physical Basis for Complex Systems ñ some propositions relating levels of organization.Ý Collective Phenomena 3:9-24.

Milgrom, Paul R., Douglass C. North and Barry R. Weingast. 1990. The role of institutions in the revival of Trade: The law merchant, private judges, and the Champagne Fairs. Economics and Politics 2:1-21.