ENTROPY and NEGENTROPY
14/05/2014 19:28
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ENTROPY and NEGENTROPY
by Paul A. LaViolette
October 1976, Portland State University
© Paul LaViolette, 2013
This unpublished paper presents a fresh perspective on the nature of entropy,
negentropy, and system morphogenesis. LaViolette shows that the concepts of
process and form provide a better context for understanding order genesis than do
concepts borrowed by convention from the field of thermodynamics.
One term which is perhaps a bit overused by general systems cosmologists is the term
"entropy". It is of particular interest because it presents the disturbing paradox that in
considering closed physical system entropy is seen to increase over time whereas in open
physical systems and living systems it appears to decrease over time. Such distinctions are good
because they are helpful in classifying system and lead the initiate to probe deeper into the
mysteries of systems metaphysics to discover a reasonable explanation.
However the term "entropy" is borrowed from the field of physics. It is normally defined in
thermodynamic terms as S = dQ/T, the change in heat (dQ) divided by the prevailing temperature
T. Its terminology was originally introduced to describe the workings of the steam engine.
Believing the principles to be of general import beyond the realm of steam engines, they were set
forth as the laws of thermodynamics. Whereupon, the Second Law, that entropy is always the
same or increases in a closed system, became philosophically taken as a universal law of
existence. The general nature of this principle became more apparent when information science
came up with the isomorphic derivation that systems of order tend toward disorder, i.e., from
states of lesser to greater probability.
It soon became obvious that entropy, whether it was increasing or decreasing or staying the
same, was an important concept for the general system theorist. The fact that the concept was
borrowed from physics or information theory does not seem to disturb the average theorist since
he can feel that he will be above criticism if he uses a term that is mathematically well
documented in respectable fields. When asked by the layman what is meant by entropy (i.e.
positive entropy), the systems theorist gives general examples like: 1) the experiment where a
sugar cube dissolves in coffee, 2) the decaying of living matter, i.e., catabolism, or 3) the running
down of a wound-up clock.
Yet, in bringing up a variety of qualitative examples such as these, it no longer makes same to
restrict the definition of entropy just to thermodynamics and information theory. A universal
conceptual symbol must be utilized. Such a symbol has already been formulated, indeed, long
ago. In fact, it dates back to antiquity. It is the esoteric meaning behind the astrological sign
Aries (), the meaning of the first arcanum of the tarot card deck (the Magician), the significance
of the male principle, yang.* In modern terminology it is the geometric concept of divergence
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* In astrology, the ideogram for Aries can be interpreted either as the rams head or as the fountain,
the tremendous outpouring of life force. Astrology holds that Aries is the pioneer. This sign is
cardinal, meaning that it initiates or generates activity. It is also a fire sign, i.e.. one expressing
dynamic creativity. Aries represents self-expression, self-projection upon the immediate
environment, and is characterized by urgency and emphasis. The Magician of the tarot, sometimes
symbolized mythologically by Mercury (the messenger) or by the dove, is characterized by similar
terms such as: beginning, potential, action, creative force, aspiration, and will power.
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(symbolized in modern mathematics by the vector operator ∇•). In the English language the
words "dispersion" and "dissemination" express the positive side of this principle, while the
word "dissipation" emphasizes the negative aspects.
In contrast to the philosophical implications of the second law of thermodynamics, the
ancients took a more or less positive view of the dispersion principle. Indeed, life and death,
degradation and creativity are two sides of the same coin. The sun may be regarded as a dying
star which is radiating away its mass; on the other hand, it may be regarded as a creative and lifegiving
force. What the sun loses, life on earth gains. When weeds invade your garden, you could
say that your neatly weeded plot goes into a state of disorder and degradation. On the other
hand, you could say that this is an example of creativity, or procreativity, plant species
propagating their kind. Here we see that dispersion is a characteristic or one aspect of the
behavior of open systems in their environment, and in this case may be found to be grounded in
biological principles.
To generalize one might say that the principle of dispersion always involves competition for
space in one way or other. In the case of compressed gas being released from a cylinder, the
cause of dispersion may be-traced to the repulsive forces developed by molecular collisions. In
the case of light radiating from a point source, dispersion is caused by the repulsive force
developed between photons whose oscillations are out of phase with one another. In the case of
catabolism, structural dispersion is caused by physical and chemical forces which
organizationally compete with an organism's anabolic processes. Anabolism can be thought of as
the building up of biological order and catabolism as the disintegration of that order. However, all
is relative. Anabolism also involves the breaking down of physical, inorganic order, and
catabolism, the reconstruction or reconstitution of that order. When a company's market share
begins disintegrating, this could be thought of as a loss of order, but for the competing companies
it seems like just the opposite.
We have demonstrated by example that the dispersion principle, with which positive entropy
is usually associated, governs both the building up and breaking down of order. Now, where does
that leave the concept of negentropy?
It is said that due to the fact that they are open systems, living organisms are capable of
decreasing their entropy, i.e., of increasing their amount of order and theirby growing. This state
of affairs, it is claimed, is due to the fact that open systems not only produce entropy, due to
irreversible processes, but also import entropy which may be negative. This proposition is
illustrated by Prigogine's Theorem,(1) stating that the variation of entropy during a time interval
dt takes the form,
dS = deS + diS , where diS ≥ 0 (1)
where deS is the flow of entropy due to exchanges with the system's surroundings and diS is the
entropy production due to irreversible processes inside the system such as diffusion, chemical
reactions, heat conduction, etc. Moreover, it is maintained that while diS must never be negative,
deS has no definite sign. So, in the case where deS is negative and greater than diS, a situation
may be obtained where dS < 0, i.e., where the net entropy of the system is negative.
Alternatively, if –deS = diS, then dS = 0, i.e., the system is maintained in a steady state.
However this model has some pitfalls. Take the example of an individual who has the choice
of eating a steak vs. eating a few hamburgers made from the same steak ground up, vs. drinking a
bouillon soup of equivalent nutrient and caloric value. For an individual to satisfy his steady
state bodily requirements, according to Prigogine's Theorem, he would not need to eat as much of
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the former as the latter ( in that sequence) since the former has a higher negentropy, i.e., greater
order. In actuality, the reverse is true; the individual has to expend more energy to digest the
steak, than the hamburger; and the nutrient broth, which can be absorbed directly in the stomach
with minimal digestion, places the least burden on the organism. Since it is calories and not
entropy which sustains the organism, one would be wiser to choose the soup.
Another problem with equation (1) is that it combines elements of both structure and
process, –deS being the import of a given quantity of structural negentropy and diS being the
entropy change due to irreversible processes in the system. While it is thermodynamically
legitimate to add these quantities, from a conceptual point of view, it is like trying to add apples
and oranges. In the end you are more confused than ever as to how open systems are able to
form ordered structures in a spontaneous manner.
The basic question remains unanswered. How does negentropy naturally arise when all
spontaneous physical and chemical processes are dissipative, i.e., characterized by entropy
increase. A system such as a cell is able to assemble macromolecules of immense complexity
creating an ordered macrolevel structure. But, at the microlevel, all the chemical processes
involved in this anabolic process are dissipative. While the mechanism of protein synthesis is
fairly well understood, the question remains; how did the phenomenon of protein synthesis first
arise? Who taught the cell this trick of generating negentropy using common every day positive
entropic processes? To avoid the pitfall of vitalism, we must conclude that this phenomenon
evolved from simple prebiotic ordering principles, and that in the course of evolution, has become
manifest in the preprogrammed and highly complex processes of the cell.
Hence, the spontaneous emergence of order at the molecular level must be a property which
is characteristic of simple open systems. Consequently, to come to an understanding of how
negentropy arises in open systems, it is best to study simple examples such as the emergence of
order in thermal convection and in nonlinear chemical reaction systems.
First, though, I will state some general laws relating to process and structural order.
1) All elemental processes are dispersive (dissipative).
2) Physical order, "negentropy" manifests at a macroscopic level when a macrolevel dispersive
process having many degrees of freedom is intersected and dominated by a macrolevel
dispersive process having two degrees of freedom. Related to this:
Order is the emergent expression of a cyclically causal phenomenon, i.e., of self-referential
causality.
In the case of thermal convection, such as that produced in a pan of water heated on a stove,
there are two elemental dissipative processes involved: a) vertical thermal convective dissipation,
and b) non-directional spatial dissipation of ordered molecular states. In the near equilibrium
regime, the homogeneous steady state condition is stable. Heat is dissipated upward via thermal
conduction. Any symmetry-breaking fluctuations, such as the formation of local pockets of
water at higher or lower densities, are damped by the random motion of the molecules., i.e.,
process b) dominates process a).
As the thermal gradient is increased, i.e., as the system is moved further from equilibrium, a
threshold is reached beyond which the symmetry of the system is broken and where thermal
convection emerges as the dominant mechanism of dissipation, i.e., process a) supercedes process
b). The transition from conduction to convection is marked by increased thermal dissipation.
Hence, in this particular example the change from one mode to the other is itself governed by the
dispersion principle.
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The thermal convection process has two mechanical degrees of freedom; see Figure 1. Either
a locally hot, low density pocket is moving up (Y1 → Y2 ), or else a locally cold, high density
pocket is moving down (X1 → X2 ). The motive force for this mechanical transport process
must be attributed to gravity. It should be mentioned that density transport implies coherent
behavior, i.e., many molecules acting in unison. To completely represent the convective cycle,
two thermal steps must also be included in which cold, high density water is transformed into
hot, low density water (X2 + Q → Y1 ), and where hot, low density water is transformed into
cold, high density water (Y2 → X1 + Q).
Figure 1
Convective dissipation, involving coherent microlevel behavior (coherent movement of water
molecules) is manifest as a macrolevel process having two degrees of freedom (flow up vs. flow
down). This-new-pattern overrides the macrolevel structural dissipation process consisting of
random microlevel processes having on the order of n directional degrees of freedom (n being the
number of molecules in a density fluctuation pocket). Hence the random symmetry of the
system is broken; the random motion of molecules is superseded by a nonrandom macrolevel
pattern. Negentropy becomes manifest. Were it not for the existence of circular causality (as
seen in Figure 1), negentropy, as manifested in the macrolevel cellular convection pattern, would
not be present. Hence it could be said that the negentropy that manifests as physical ordering
was already preexistent in the circular structuring of causation or process. Therefore,
negentropy, structure, and form should be associated with the geometric principle of self-closure
(mathematically symbolized by the vector operator ∇×, or curl). This illustrates how physical
form emerges from behavioral patterning.* Floyd Allport(2) has brilliantly developed a theory of
behavioral form in his event-structure theory, and this may be usefully applied here.
Nonlinear open chemical system also exhibit ordering properties. Take for example the
following reaction scheme suggested by Glandsdorff and Prigogine:(3)
(A held constant) A → X (i)
2X + Y → 3X (ii)
B + X → Y + D (iii)
X → E . (iv)
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* Applied to social systems, this approach illustrates how the physical aspects of social systems (such
as technological devices, buildings, land use patterns, etc.) emerge from human behavior patterns
governed at the symbolic level by values, norms, beliefs, and roles.
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Figure 2
In the near-equilibrium regime, with the input of B maintained at a reduced level, the
homogeneous steady state condition is stable. Equations i) and iv) predominate such that A →
X → E appears as the primary global reaction. At low concentrations of B the overall reaction B
→ D remains in the near equilibrium regime, hence the autocatalytic steps, equations ii) and iii),
remain insignificant. Any tendency for inhomogeneities to develop due to steps ii) and iii) is
damped by the random motion of the molecules, appearing as a dissipative process at the
macromolecular level.
However, as the concentration of B is increased, that is, as the reaction B → D moves far
from equilibrium, a threshold is reached where equations ii) and iii) become significant. The
homogeneous steady state maintained by random motion becomes superseded, wherein, the
system begins to exhibit coherent temporal ordering, i.e., concentrations of X and Y at the
microlevel coherently oscillate periodically with respect to each other. Due to molecular
diffusion, this temporal ordering of chemical composition becomes manifest as spatial ordering in
the reaction volume, wherein shells of alternating X, Y concentration expand outward from the
location of the initial instability, invading the surrounding homogeneous medium with a
spherically symmetric periodic structure. These shells may themselves be static or propagating.*
The oscillating reaction system has at the microlevel two degrees of freedom: a state of either
more of X and less of Y, or a state of more of Y and less of X. This inherent dichotomy becomes
magnified and expressed as coherent behavior at the multi-molecular macro level due to the
presence of the autocatalytic step ii) and diffusion.
Unlike the convection example, the existence of circular causality is here not alone sufficient
to manifest ordering. This is because the circular causal process here takes place at a microlevel
uniformly throughout the reaction volume. It is not until this circular causality becomes
integrated via diffusion and step ii) to produce coherent oscillations that it is able to become
manifest as spatial ordering at the multi molecular level. Hence, a universal criterion for the
emergence of order in either type of open system is the emergence of macrolevel circular causal
behavior, i.e., coherent circular causal behavior at the microlevel dominating the tendency toward
homogeneity.
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* Note that this reaction scheme is only theoretical, being chemically impossible due to the tri
molecular reaction in step ii).
[Update] Nevertheless, Lefever, et al. (1988) later showed that trimolecular reaction (ii) can be
expanded into two coupled bi-molecular reactions. [Lefever, R., Nicolis, G., and Borckmans, P.
"The Brusselator: It does oscillate all the same." J. Chem. Soc. Faraday Trans. 1 84 (1988): 1013-
1023.]
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What is typically termed positive entropy is simply the tendency for random microlevel
behavior, or chaos, to supplant microlevel coherent behavior. This microlevel behavior is so
complex by virtue of its numerous degrees of freedom that it appears at the macrolevel as
homogeneous order (like "snow" noise on a TV screen). What is typically termed negative
entropy is simply macrolevel order, i.e., the replacement of microlevel chaotic behavior by
microlevel coherent dichotomous behavior, the latter incorporating circular causality.
Positive entropy, therefore, should be conceptually associated with process, the dispersion
principle, while negative entropy should be associated with form, or the circular causality
principle, wherein two or more dispersive processes are organized into a self-closing loop.
References
1) Prigogine, I., Etude Thermodynamigue des Phenomenes Irreversibles, Desoer, Liege (1947).
2) Allport, F.,"The structuring of events: Outline of a general theory with applications to
psychology", Psychological Review, 61, p. 281, (1954).
3) Glansdorff, P. and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations,
Wiley, New York (1971).
This paper was written for a systems science class taught by Ervin Laszlo. After reading the
paper, Prof. Laszlo wrote at the end of the paper the following comment:
"So, in evolution form is imposed on process -- pure Aristotle. Applications to coupled
systems. Implications of "form" as a general category need to be worked out.
