Translation
of physics articles by Soodak and Iberall in our reader Chapter 3 (Chs. 24 and 27 in Yates' Self-Organizing
Systems.İ 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.İ
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.İ 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.İ
Why
do I care about these articles in particular?İ
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.İ 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.İ Typically, processes occur as a function of
gradients from point to point in some field, where interaction leads to the
equipartition of energies.İ For
example:İ 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).İ
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 ñİ 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=mc^{2}).İ
--
-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- -- -- --
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).İ 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.İ
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.İ H is the capacity of
energy differentials to diffuse heat (relative to a surrounding) or to do work.İ (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.İ
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).İ 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).İ 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).İ
Corollaries: (1)İ 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.İ 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.İ
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.İ 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.İ The logarithm of that number [ln W] of ways
is the entropy" (Feynmann 1963 vol. 3 section 46-5).İ 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.İ (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*).İ Claude Shannon used the term entropy to
refer to disorder in information.İ 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"?İ 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). Wolfísİ 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:
İİİİİ "In this dissertation the question of how information is carried in a physical system is examined. The systems studied here
İİİİİ are simple, as are all systems which have a presentable analysis. The point of view that the states of the physical system of
İİİİİ interest may be treated probabilistically, that there is an underlying distribution which describes the probability that a
İİİİİ 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).İİ Does
their wariness imply that all organisms equally highly evolved (Margulis
and Sagan 1995:44)?İ 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.İ Any system that is not at
thermal equilibrium has organized
gradients of energy, and these gradients necessarily depend on energy
inputs from its surroundings.İ
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.İ The
universe is full of embedded systems, like Chinese dolls.
İİİİİİ
example:İ 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:İ 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.İ 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").İ That
is the key to understanding evolution.İ
All kinds of embedded systems evolve, living and nonliving.İ 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-observationİ
based social science that is scientifically grounded.
Ch. 24. Soodak and
Iberall.İ 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
İİ windup of galaxies -> condense to create
İİİİİ explosion of stars -> convert
İİİİİİİİ hydrogen into more complex molecules
= that form
İİİİİİİİİİ more diverse forms of matter ->
condense into
İİİİİİİİİİİİİİ planetary systems -> support
İİİİİİİİİİİİİİİİİ planetary geochemistries
-> support
İİİİİİİİİİİİİİİİİİİİ origins of diverse forms
of life -> which serve as
İİİİİİİİİİİİİİİİİİİİİİİ platforms for more
complex forms of life -> that form
İİİİİİİ İİİİİİİİİİİİİİİİİİİall 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.İ pp. 460-461:İ "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."İ 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.İ 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."İ 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.İ 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).İ
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].İ
…
by
directed movements at a constant inertial velocity (called convection) of coherent ensembles of molecules or atomisms.İ 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.İ 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.İ 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.İ 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).İ 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_{o}^{2}
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,
İİİİ Re = (L_{o}^{2} r/m) / (L_{o}/V) = L_{o}Vr/m
İİİİİİİİİİ = time to diffuse a distance L_{o} / time to convect a distance L_{o}
İİİİİİİİİİ = Velocity V (convection) / Velocity v (diffusion)
= (L_{o}V) /(m/r)
İİİİİİ < 1 diffusion time can handle
convective flow, no structural change
İİİİİİ = 1 transition from microscopic
transport to macroscopic transport
İİİİİİ > 1 when diffusion time too short to
handle convection, structural change
İİİİİİ 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.İ 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 ...İİİİİİİİİİİİİ
Higher likelihood of transition if ...
V=velocity
of some incoming flowİİİİİİİİİİİİİİİ
...more stress on a system
with..
v=velocity
of diffusionİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİ
Öslower diffusive velocity withÖ
t(tau)= average time between
collisionsİİİİİİİ ...less time between collisions,
vt=diffusive movement in time unit tİİİİİİİİİİİİ
Öless distance between collisions,
L_{o}=diameter
of atomistic cellsİİİİİİİİİİİİİİİİİİİİİİİ
...bigger atomisms that areÖ
r(rho)=density of the atomism
or networkİİİİ ...more dense, withÖ
c=
speed of propagation through fluid, netwk ...less propagative dissapation,
İİİ (via sound vibration), andÖ
m(mu)=shear viscocity = r t c^{2}İİİİİİİİİİİİİİİİİİİİİİİ ...less sticky with one another.
İİİ (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.İ 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:
İİİİ N > (vt/VL_{o})^{2 }
İİİİ 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.İ
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.İ
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_{o}V/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.İ Here, the minimum
number of interacting centers is Nª16.İ 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.İİ
Table 1: Stability
Transitions |
generational relaxation time t (days) |
cell diameter L_{o} (miles) |
convective velocityİ V (miles/day) [trade, husb.] |
viscous velocity v (miles/day) |
Re > 1İİ _ İİİİİİİİ =÷N(VL_{o}/vt) \ Nİİ >İİİ (vt/L_{o}V)^{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} |
İ 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.İ 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.îİ 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.îİ 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).İ
Those are exactly the kinds of dynamical processes we expect in a
Reynolds phase transition.İ 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
stabilizedİ 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.İ You can see if there are any parts of Ch. 27
that now make sense to you.İ It is still
tough going.]
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.İ 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.