Modern Trends in BioThermoKinetics 3, 50-61, 1994.
What is (Schrödinger's) Negentropy?
Walton Hall, Milton Keynes
MK7 6AA, U.K.
I attempt to outline, qualitatively, a 'thermodynamics of organized
complexity' based on energy storage and mobilization in a coherent
space-time structured system maintained far from thermodynamic equilibrium
by energy flow. I propose that symmetrically coupled cycles will arise in
open systems capable of energy storage, and that for such systems, the
equal population of energy over all space-time domains (the 'k =
const.' regime) is the extremum state. This regime is characterized by the
maximum of the Gibbs entropy function,
ln pj, in
which the potential degrees of freedom are maximized over all space-time
domains, but it is also the state of minimum entropy because the
activities in all space-time domains are effectively coupled to a single
actual degree of freedom.
'Negentropy', living organization, space-time structure, stored energy,
coherence, coupled cycles, thermodynamics of organized complexity.
Is It Free Energy?
The 'negentropy', or 'negative entropy', that I am thinking of, comes
from Schrödinger's book, What is Life?1,
in which he writes,
"It is by avoiding the rapid decay into the inert state of
'equilibrium' that an organism appears so enigmatic....What an organism
feeds upon is negative entropy."
In a footnote, later, however, Schrödinger explains that by
'negative entropy', he really means free energy. Many subsequent
authors have taken negentropy as being simply entropy with a negative sign2,3,
as they feel it simply is erroneous to refer to 'negentropy' as free
Despite that, the term continues to be used by biologists to the present
day, beginning with one of the most authoritative among them:
"It is common knowledge that the ultimate source of all our energy
and negative entropy is the radiation of the sun."4
The reason 'negentropy' continues to be used is that 'entropy with a
negative sign' simply does not capture what is intended by the original
term. Schrödinger uses it to identify the remarkable ability of the
living system, not only to avoid the effects of entropy production - as
dictated by the second law - but to do just the opposite, to increase
organization, which intuitively, seems like the converse of entropy.
Szent-Györgi, on the other hand, alludes to both the notions of free
energy and of organization in his use of the term. Both scientists have
the right intuition - energy and organization are inextricably bound up
with each other.
Within biological science, free energy is generally regarded the most
relevant for biochemical reactions. The change in free energy being,
The energy content of the system is thereby partitioned into the
entropic term, which is related to the random thermal motion (molecular
chaos) of the molecules that is somehow not available for work,
and tends to disappear at absolute zero temperature, and the free energy,
which is somehow available for work. But as there need be no
entropy generated in adiabatic processes - which occur frequently in
living systems (see below) - the division into available and nonavailable
energy cannot be absolute: in other words, the energy associated with a
molecule simply cannot be partitioned into the two categories a priori.
Is It Maxwell's Demon?
The second law of thermodynamics is a statistical law which applies to a
system consisting of a large number of particles. A major difficulty,
already noticed by Schrödinger, is that single molecules, or a very
small number of them, are the active agents in living systems. Thus, each
cell contains only one or two molecules of each sequence of DNA in the
nucleus. Similarly, it takes no more than several molecules of a hormone
to bind to specific receptors in the cell membrane in order to initiate a
cascade of biochemical reactions that alter the characteristics of the
whole cell. Does that mean the second law cannot be applied to living
This difficulty is related to the problem of Maxwell's demon5
- an hypothetical intelligent being who can open a microscopic trapdoor
between two compartments of a container of gas at equilibrium in order to
let fast molecules through in one direction, and the slow ones in the
other, so that work can then be extracted from the system. It became
evident in the 1950s that something like a Maxwell's demon could be
achieved with little more than a trapdoor that opens in one-direction only
and requires a threshold amount of energy (activation energy) to open it.
This is realizable in solid-state devices such as diodes and transistors
that act as rectifiers5.
Similar situations are associated with biological membranes, which play
a major role in structuring biological systems. Typically, an electrical
potential gradient of some 107V/m is maintained
across membranes, embedded in which are enzymes involved in the vectorial
transport of ions and metabolites from one side to the other, as for
example, the transport of Na+ out of, and K+
into the cell by the Na+/K+
ATPase. It has recently been demonstrated that weak alternating electric
fields can drive unidirectional active transport by this enzyme without
ATP being broken down. In other words, the energy from the electric field
is directly transduced into transport work by means of the membrane-bound
enzyme. Moreover, randomly fluctuating electric fields are also effective,
precisely as if Maxwell's demon were involved in making good use of the
fluctuations6! Of course, there is no real
violation of the second law, for rectifiers and biological membranes are
both non-equilibrium structures which can store energy.
The problem of Maxwell's demon is generally considered as having been
'solved' by Szilard, and later, Brillouin2, who
showed that the demon would require information about the
molecules, in which case, the energy involved in obtaining information
would be greater than that gained and so the second law remains inviolate.
Perhaps, what they have failed to take account of is that the so-called
information is already supplied by the special structure or organization
of the system in which energy is stored. Biological membranes, in
particular, are excitable structures poised for relaying and
amplifying weak signals into the cell.
Is It Organization?
An organism is nothing if not organized heterogeneity, with nested
dynamic structures over all space-time scales. There is no homogeneity, no
static phase held at any level. Even a single cell has its characteristic
shape and anatomy, all parts of which are in constant activity; its
electrical potentials and mechanical properties similarly, are subject to
cyclic and non-cyclic changes as it responds to and counteracts
environmental fluctuations. Spatially, the cell is partitioned into
numerous compartments by cellular membrane stacks and organelles, each
with its own 'steady states' of processes that can respond directly to
external stimuli and relay signals to other compartments of the cell.
Within each compartment, microdomains can be separately energized to give
local circuits, and single enzyme proteins, or complexes of two or more
proteins function as 'molecular machines' which can cycle autonomously
without immediate reference to its surroundings.
In other words, the steady 'state' is not a state at all but a
conglomeration of processes which are spatiotemporally organized, ie, it
has a deep space-time structure, and cannot be represented as an
instantaneous state or even a configuration of states7.
Characteristic times of processes range from <10-14
s for resonant energy transfer between molecules to 107
s for circannual rhythms. The spatial extent of processes, similarly, span
at least ten orders of magnitude from 10-10 m for
intramolecular interactions to metres for nerve conduction and the general
coordination of movements in larger animals.
The processes are also catenated in both time and space: the
extremely rapid transient flows (very short-lived pulses of chemicals or
of energy) triggered on receiving specific signals, are propagated to
longer and longer time domains of minutes, hours, days, and so on via
interlocking processes which ultimately straddle generations. The
processes, rather than constituting the system's 'memory' as we might
think, are actually projections into the future at every stage.
They determine how the system responds and develops in times to come.
Typically, multiple series of activities are initiated from the focus of
excitation. While the array of changes in the positive direction is
propagating, a series of negative feedback processes is also spreading,
which has the effect of dampening the changes. It is necessary to think of
all these processes cascading in parallel in many dimensions of
space and time. In case of disturbances which have no special significance
for the body, homeostasis is restored sooner or later as the disturbance
passes. On the other hand, if the disturbance or signal is significant
enough, a series of irreversible events brings the organism to a new
'steady state' by developing or differentiating new tissues. The organism
may even act to alter its environment appropriately8.
The secret of 'negentropy' lies undoubtedly in this intricate space-time
organization. But how can one describe it in terms of the second law?
As living systems consist of nested space-time compartments of various
sizes, all the way down to microdomains and molecular machines, then at
the very least, this implies that if thermodynamics were to apply to
living systems, it must apply to individual molecules as much as to
ensembles of molecules. Such is the physiologist Colin McClare's
Is It Stored Energy?
In order to formulate the second law of thermodynamics so that it
applies to single molecules, McClare introduces the important notion of a
characteristic time interval, t, within which a system reaches
equilibrium at temperature q.
The energies contained in the system can be partitioned into stored
energies versus thermal energies. Thermal energies are those that
exchange with each other and reach equilibrium in a time less than
(so technically they give the so-called Boltzmann distribution
characterized by the temperature
Stored energies are those that remain in a non-equilibrium
distribution for a time greater than t, either as characterized by
a higher temperature, or such that states of higher energy are more
populated than states of lower energy. So, stored energy is any form which
does not thermalize, or degrade into heat in the interval t.
Stored energy is not the same as free energy, as the latter
concept does not involve any notion of time. Stored energy is hence a more
McClare goes on to restate the second law as follows: useful work
is only done by a molecular system when one form of stored energy is
converted into another. In other words, thermalized energy is unavailable
for work and it is impossible to convert thermalized energy into stored
The above restatement of the second law is unnecessarily restrictive,
and possibly untrue, for thermal energy can be directed or
channelled to do useful work in a cooperative system, as in the case of
enzymes embedded in a membrane7, which can undergo
correlated motions. Thermalized energy from burning coal or petrol is
routinely used to run machines such as generators and motor cars (which is
why they are so inefficient and polluting).
A more adequate restatement of the second law, which can apply to single
molecules as well as ensembles of molecules, I suggest, might be as
Useful work can be done by molecules by a direct transfer of stored
energy, and thermalized energy cannot be converted into stored energy.
The second half of the statement accounts for entropic decay as is usual
in real processes both inside and outside the living system. The first
half, however, is new and significant for biology.
The major consequence of McClare's ideas arises from the explicit
introduction of time, and hence time-structure. For there are now
two quite distinct ways of doing useful work, not only slowly according to
conventional thermodynamic theory, but also quickly - both of which are
reversible and at maximum efficiency as no entropy is generated. This is
implicit in the classical formulation, dSe0, for which the limiting case
is dS=0. But the attention to time-structure makes much more precise what
the limiting conditions are. Let us take the slow process first. A slow
process is one that occurs at or near equilibrium. According to classical
thermodynamics, a process occuring at or near equilibrium is reversible,
and is the most efficient in terms of generating the maximum amount of
work and the least amount of entropy. By taking explicit account of
characteristic time, a reversible thermodynamic process merely needs to be
slow enough for all thermally-exchanging energies to equilibrate, ie,
slower than t, which can in reality be a very short period of
time, for processes that have short time constants. Thus, for a process
that takes place in 10-12s, a microsecond (10-6s)
is an eternity! So high efficiencies of energy conversion can still be
attained in thermodynamic processes which occur quite rapidly, provided
that equilibration is fast enough. This may be where spatial partitioning
and the establishment of microdomains is crucial for restricting the
volume within which equilibration occurs, thus reducing the equilibration
time. This means that local equilibrium may be achieved at least for
some biochemical reactions in the living system. We begin to see that
thermodynamic equilibrium itself is a subtle concept, depending on the
level of resolution of time and space.
At the other extreme, there can also be a process occurring so quickly
that it, too, is reversible. In other words, provided the exchanging
energies are not thermal energies in the first place, but remain stored,
then the process is limited only by the speed of light. Resonant energy
transfer between molecules is an example of a fast process. It occurs
typically in 10-14s, whereas the molecular
vibrations themselves die down, or thermalize, in 10-9s
to 101s. It is 100% efficient and highly specific,
being determined by the frequency of the vibration itself; and resonating
molecules (like people) can attract one another.
Does resonant energy transfer occur in the living system? McClare9
suggests it occurs in muscle contraction, where it has been shown that the
energy released in the hydrolysis of ATP is almost completely converted
into mechanical energy in a molecular machine which can cycle autonomously
without equilibration with its environment. Similar cyclic molecular
machines are involved in other major energy transduction processes: in the
coupled electron transport and ATP synthesis in oxidative phosphorylation
and photophosphorylation, as well as in the Na+/K+
ATPase. Ultrafast, possibly resonant energy transfer processes are also
operating in photosynthesis. There, the first step is the separation of
positive and negative charges in the chlorophyll molecules of the reaction
centre, which has been identified11 to be a readily
reversible reaction that takes place in less than 10-13s.
McClare's ideas have been taken up and developed by Gonda and Gray12,
Blumenfeld13, and more recently, Welch and Kell14,
among many others, particularly in the notion of nonequilibrium, 'quantum
molecular energy machines'. These ideas imply that the living system may
use both means of efficient energy transfer: slow and quick reactions,
always with respect to the relaxation time, which is itself a variable
according to the processes and the spatial extents involved. In other
words, it satisfies both quasi-equilibrium and far from equilibrium
conditions where entropy production is minimum. This insight is offered by
taking into account the space-time structure of living systems explicitly.
Are we getting closer to the source of 'negentropy' in living systems?
Stored Energy versus Free Energy
It is of interest to compare the thermodynamic concept of 'free energy'
with the concept of 'stored energy'. The former cannot be defined a
priori, much less can it be assigned to single molecules, as even
changes in free energy for an ensemble cannot be defined unless we know
how far the reaction is from equilibrium. 'Stored energy', as defined by
McClare with respect to a characteristic time interval, can readily be
extended, in addition, to a characteristic spatial domain. We can
generalize it to stored energy within a characteristic space-time.
As such, it is explicitly dependent on the space-time structure of the
system, and hence, it is a precise concept which can be defined on the
space and time domain of the processes involved. Indeed, stored energy has
meaning with respect to single molecules in processes involving quantum
molecular machines as much as it has with respect to the whole organism8.
For example, energy storage as bond vibrations or as strain energy in
protein molecules occurs within a spatial extent of 10-9
to 10-8m and a characteristic timescale of
10-9 to 10-8s20.
In terms of a whole organism such as a human being, the overall energy
storage domain is in metre-decades.
Can one now offer a tentative answer to the question. "What is
negentropy?" Isn't 'negentropy' simply stored, mobilizable energy?To
work out how energy is stored and mobilized is the beginning of a
'thermodynamics of organized complexity' which could be applied to living
systems. I shall sketch out a few preliminary, qualitiative ideas in the
last section, some of which are dealt with in greater detail in my recent
Towards a Thermodynamics of Organized Complexity
1. Coupled cycles
Significant advances in our understanding of living systems began with
the thermodynamics of open systems. The quasi-equilibrium approximations
of the steady state developed by Onsager and Denbigh show how symmetrical
coupling of linear processes can arise naturally in a system under
energy flow15,16. A system of many coupled
processes can be described by a set of linear equations,
Ji = Sk
where Ji is the flow of the ith
process (i = 1, 2, 3.....n), Xk is the kth
thermodynamic force (k = 1, 2, 3,.....n), and Lik
are the proportionality coefficients (where i = k) and coupling
coefficients (where i ` k). Onsager showed that for such a multicomponent
system, the couplings for which the Xks are
invariant at microscopic level with time reversal (i.e., velocity
reversal) will be symmetrical; in other words,
The mathematical entities of the Onsager's thermodynamic equations of
motion can all be experimentally measured and verified, although the
approach has not yet been systematically applied to the living system.
Nevertheless, it captures a characteristic property of living systems: the
reciprocal coupling of many energetically efficient processes: for
example, ATP synthesis from ADP and Pi is coupled to electron/proton
transport in oxidative phosphorylation, and ATP splitting is coupled to
the translational movements between myosin and actin binding sites in
muscle contraction8. In both cases, the reactions
are completely reversible: ATP can be split into ADP and Pi by the ATP
synthesizing enzyme when the electron/proton gradients are run in reverse.
Similarly, ATP is synthesized by the myosin ATPase when ADP and Pi is
Another important development in the thermodynamics of the steady state
came from Morowitz, who derived a theorem showing that at steady state,
the flow of energy through the system from a source to a sink will lead to
at least one cycle in the system17. For a canonical
ensemble of systems at equilibrium with i possible states, where
fi is the fraction of systems in state
i (also referred to as occupation numbers of the state i), and
tij is the transition probability that a
system in state i will change to state j in unit time. The
principle of microscopic reversibility requires that every forward
transition is balanced in detail by its reverse transition, ie,
= fj tji
If the equilibrium system is now irradiated by a constant flux of
electromagnetic radiation such that there is net absorption of photons by
the system, i.e., the system is capable of storing energy, a
steady state will be reached at which there is a flow of heat out into the
reservoir (sink) equal to the flux of electromagnetic energy into the
system. At this point, there will be a different set of occupation numbers
and transition probabilities, fi' and tij';
for there are now both radiation induced transitions as well as the random
thermally induced transitions characteristic of the previous equilibrium
state. This means that for some pairs of states i and j,
For, if the equality holds in all pairs of states, it must imply that
for every transition involving the absorption of photons, a reverse
transition will take place involving the radiation of the photon such that
there is no net absorption of electromagnetic radiation by the system.
This contradicts the original assumption that there is absorption of
radiant energy (see previous paragraph), so we must conclude that the
equality of forward and reverse transitions do not hold for some pairs of
states. However, at steady state, the occupation numbers (or the
concentrations of chemical species) are time independent (ie, they remain
constant), which means that the sum of all forward transitions is
equal to the sum of all backward transitions, ie,
dfi'/ dt = 0 = S (fi'tij'
But it has already been established that some fi'tij'
are non-zero. That means other pairs must also be non-zero to
compensate. In other words, members of the ensemble must leave some states
by one path and return by other paths, which constitutes a cycle. Hence,
in steady state systems, the flow of energy through the system from a
source to a sink will lead to at least one cycle in the system.
The two results - Onsager's reciprocity relationship and Morowitz'
theorem of chemical cycles - I believe, imply a third: that symmetrically
coupled cycles will arise in open systems which are capable of
storing energy under energy flow8. Coupled cycles
are the stuff of living organization, as a most cursory glance at a
metabolic chart of 'biochemical pathways' will immediately reveal to us.
It is how living systems store and mobilize energy: the energy yielding
cycles are almost always coupled to energy requiring ones so that energy
can be transferred to larger and larger space-time domains. (And as
mentioned above, symmetrical coupling is indeed the rule for the
energetically most efficient processes in the living system.) Thus, the
energy of the photon absorbed by chlorophyll in green plants goes to
reduce NADP and to make ATP, which in turn goes to make carbohydrates,
fats, proteins and nucleic acids with increasingly longer turnover times
and wider distributions.
2. Dissipative structures are coupled cycles
Coupled cycles actually also appear in the nonlinear regime8,
in dissipative structures, arising in systems maintained far from
thermodynamic equilibrium by energy flow. A nonlinear generalization of
the Onsager reciprocity relation has recently been obtained by Sewell for
a class of irreversible processes in continuum mechanics18,
suggesting that symmetrical coupling may also be important for dynamical
stability in the far from equilibrium regime. A well-studied example of a
dissipative structure is the Bénard convection cells which form in
a shallow pan of water, heated uniformly from below, as a critical
temperature difference is reached between the top and the bottom of the
pan. At that point, the hotter, and therefore, lighter water at the bottom
rises to the top while the denser water at the top sinks to the bottom,
and so on in a cyclic manner, resulting in a convection flow cell. Soon,
the water in the entire pan become convection cells, all of the same size
and cycling together, giving a regular honey-comb appearance when viewed
from the top. The resulting dissipative structure represents a
nonequilibrium phase transition to macroscopic order. It has a dynamic
stability suggestive of that in living systems, which depends on the
coupling of cyclic processes, in this case, heat flow being coupled to the
convectional movement of molecules.
3. Dissipative structures are coherent structures
Dissipative structures are also coherent structures in which a
system with an astronomical number of potential degrees of freedom
settles into a single actual degree of freedom. It is
anti-statistical, collective activity generating long-range dynamical
Laser action is yet another example of condensation into a collective
mode of activity when energy pumping into the system exceeds a certain
threshold. Based on these analogies, Fröhlich19
predicts that as a living organism is made up predominantly of dielectric
molecules packed rather densely together, it may represent a special solid
state system where electric and viscoelastic forces constantly interact.
Under those conditions, metabolic pumping results in condensation to
collective modes of activity or 'coherent excitations', giving macroscopic
order and coordination to the living system. Fröhlich's hypothesis
has been developed by others since20,21. Duffield21,
in particular, proves that the 'Fröhlich state' is an asymptotically
stable global attractor. There is, indeed, a growing body of experimental
evidence for coherence and cooperativity at different levels within living
systems: from the action of enzymes22, to whole
organisms23 and populations of organisms24,25.
The enzyme molecule is now known to be much more mobile than previously
thought: with peptide bond vibrating, deforming, hydrogen bonds breaking
and forming, entire domains of the protein macromolecule contracting and
expanding, and the polypeptide chain unfolding and refolding over a wide
range of time-scales from 10-14s to seconds and
even minutes. Enzyme catalysis depends on the very rapid 'fluctuations' as
the protein samples its 'conformational space' in the context of its
micro-environment, so that the single trajectory corresponding to
efficient enzyme action can be readily accessed in a coherent, or highly
cooperative way over the whole of the macromolecule. (For details, readers
should consult the excellent collection of papers in ref.26.)
One of the predictions of Fröhlich's hypothesis of coherent
excitations is extreme sensitivity to weak electromagnetic fields, which
can precipitate specific coherently excited states or interfere with their
formation at phase transition. In my laboratory, we have found that brief
exposures of early fruitfly embryos to weak static magnetic fields cause
characteristic global perturbations to the segmental body pattern of the
larvae emerging 24 hours later27.28. The
abnormalities are reminiscent of the fluid dynamical patterns obtained in
a typical Couette-Taylor experiment, and also similar to the pattern
defects that can arise in phase ordered liquid crystals (I thank Ian
Stewart for pointing this out to me). Indeed, we have recently succeeded
in imaging live organisms by visualizing coherent liquid crystalline
mesophases of molecules making up the living tissues8,29,30.
A particularly interesting finding is that for all organisms, from
protozoa to vertebrates without exception, the anterior-posterior axis of
the body is also the major polarizing axis for all of the tissues. This is
quite compelling evidence for some kind of globally coherent polarizing
field, which not only gives rise to the major body axis, but also
phase-order the molecules all over the body.
4. Coupled cycles, space-time structure, energy storage and coherence
Coupled cyclic processes structure space and time for energy storage and
mobilization. In the Bénard convection cells, heat energy is stored
in the hot water at the bottom, which is used to perform the 'work'
involved in bulk flow. By extrapolation, we can think in terms of the
organism as a nested structure of coupled cycles within coupled cycles
spanning the entire range of characteristic space-time domains. One of the
most distinguishing feature of the organism - of 'living stuff' as opposed
to a 'man-made machine' such as a computer - is that it is thick with
activities over all space-time scales (c.f. Havel's concept that the
density of interacting levels is a distinguishing feature of organisms31.)
Its energy storage is correspondingly distributed over the entire range of
space-time domains in a readily mobilizable form through coupled,
catenated cycles. The reason organisms can respond so promptly and
mobilize energy at will is because energy is instantly available in the
short-term stores. The ATP 'energy debt' in our muscles, for example, is
seldom allowed to accumulate, as it is immediately replenished by creatine
phosphate and by breaking down glycogen, these latter energy stores taking
increasingly longer times to replace. It is in this way that the organism
can effectively achieve a single degree of freedom as consistent with
coherence and living organization.
Coherence in a space-time structured system is a transparency of energy
and information transfer throughout the entire system. It has many
interesting implications, some of which are explored in my recent book8.
The most obvious implication is that our actions are invariably space-time
cascades differing in extents and durations from the microscopic through
the mesoscopic to the macroscopic. It is an intriguing thought that the
usual distinction between quantum and classical (or microscopic versus
macroscopic) phenomena may only be a illusion of scale. The so-called
'collapse of the wave function' associated with a macroscopic measurement
process may be the result of a space-time cascade reaching the
characteristic dimensions of our everyday awareness, which, nevertheless,
remains 'quantum' to an observer of galactic dimensions. The possibility
for observing 'macroscopic quantum coherence' has been considered by a
number of physicists who question the usual distinction between the
quantum and the classical domains (see ref. 32).
5. The k=const. regime and the extremum state for organized open systems
The thermodynamics of organized complexity thus involves energy storage
and mobilization spanning the entire nested hierarchy of space-time
domains. I have arrived at this conjecture via another route, but it is,
in effect, a generalization of Popp's discovery, from his many years of
experimentation on light emission from living organisms: that photons are
stored in living organisms with equal population over all frequencies, for
which he proposed the 'f=const. rule'33. Popp and
many others since, have found that all organisms emit light ('biophotons')
at ultraweak intensities from a few photons per cell per day to several
hundred photons per organism per second, which are strongly correlated
with the cell cycle and other functional states34.
The emitted light typically covers a wide band (200nm to 900nm) around the
optical range - the limitation being usually set by the photon-detecting
device - with approximately equal number of photons throughout the range,
thus deviating markedly from the Boltzmann distribution characteristic of
a system at thermodynamic equilibrium.
Biophotons can also be studied as stimulated emission after a brief
exposure to light of different spectral compositions. It has been found,
without exception that the stimulated emission decays, not according to an
exponential function characteristic of non-coherent light, but rather, to
a hyperbolic function which is, according to Popp and Li, a sufficient
condition for a coherent light-field35. What this
implies is that photons are held in a coherent form in the organism, and
when stimulated, they are emitted coherently, like a very weak, multimode
laser. Such a multimode laser has not yet been made artificially, but it
is at least not contrary to the theory of coherence in quantum optics as
developed especially by Glauber36, so long as
the modes are coupled together.
There is, indeed, evidence that the modes within the visible range are
coupled together. Spectral analysis of the emission stimulated by
monochromatic light or light of restricted spectral compositions show that
the hyperbolic decay kinetics is uniform throughout the visible spectrum37.
The stimulated emission always covers the same broad range, regardless of
the composition of the light used to induce it, and furthermore, can
retain its spectral distribution even when the system is perturbed to such
an extent that the emission intensity changes over several orders of
magnitude. These observations are consistent with the idea that the living
system is one coherent 'photon field' bound to living matter. This photon
field is maintained far from thermodynamic equilibrium, and is coherent
simultaneously in a whole range of frequencies that are nonetheless
coupled together to give, in effect, a single degree of freedom. This
means that random energy input to any frequency will become delocalized
over all frequencies, precisely as predicted in a system in which energy
is stored and mobilized over all space-time domains.
The equal population of space-time photons (or energy) may be referred
to as the 'k=const. regime'. The significance of this regime is that it
may be the extremum state towards which all open systems - capable of
storing energy - evolve. The Gibbs entropy function of the system,
reaches a maximum when all the
Let us dwell on this further, as it may be the key to living
organization and 'negentropy'. The k=constant regime is the maximum
entropy state in which the potential degrees of freedom are
maximized over all space-time domains, but, for living systems, it is also
the state of minimum entropy because the activities in all space-time
domains are effectively coupled so there is only a single actual degree of
freedom33. Formally, it has the characteristics of
the '1/f noise' identified in systems exhibiting so-called 'self-organized
criticality' by Bak and his coworkers38, who
demonstrated that large interactive dynamical systems typically
self-organize into a globally correlated 'critical' state far from
equilibrium. This critical state is highly sensitive, in that a small
local event can lead to large 'avalanches' of activity spreading
throughout the system, when self-similarity in activities occur over all
space and time scales. The theory claims to provide a natural explanation
of a number of physical and geophysical intermittent phenomena, including
earthquakes, volcano eruptions, solar flares, noice in electronic
circuits, economics and patterns of species extinction in evolution. The
parallel with the picture of the living system that we have described is
striking. This very same state can also be described in terms of the coherent
quantum state or 'pure' state in which all possibilities are
superposed and immediately accessible8,39. The
adaptability of the organism depends on just this seemingly paradoxical
property. For, only by maximizing the potential degrees of freedom is it
possible to access the single degree of freedom that is required for
'Negentropy', as stored mobilizable energy in a space-time
structured (organized) system, can be intuitively understood as
follows. In an equilibrium system, energy is fixed, which in turn fixes
the population of energy levels characteristic of the temperature of the
system. In a nonequilibrium system such as the organism, energy is stored
over all space-time domains. For a given temperature, the energy stored is
no longer fixed, but on account of efficient coupling, becomes transferred
to ever larger space-time domains (starting from the photon trapped in
photosynthesis, or the energy in food) until all characteristic domains
are equally populated. This implies that the organism itself has no
preferred levels, its activities spanning the 'quantum' to 'classical',
from the 'microscopic' through 'mesoscopic' to the ' macroscopic' in a
quasi-continuum of self-similar patterns.
Some of the ideas for this article grew out of extensive, though
intermittent, discussions with Fritz Popp over a period of the past four
years. I have also profited substantially from recent correspondences with
Kenneth Denbigh and Oliver Penrose, and recent conversations with Ivan
Havel, Basil Hiley and Chris Dewdney. Much thanks to Geoffroy Sewell and
Kenneth Denbigh for commenting on earlier drafts of this manuscript.
Geoffroy Sewell, in particular, gave me several stimulating tutorials over
the telephone. None of those mentioned should be held responsible for my
1. E. Schrödinger What is Life? Cambridge University Press,
2. L. Brillouin, L. Science and Information Theory, 2nd ed.,
Academic Press, New York, 1962.
3. Penrose, O. Foundations of Statistic Mechanics, A
Deductive Approach, Pergamon Press, Oxford, 1970.
4. A. Szent-Györgi, A. An Introduction to Submolecular Biology,
Academic Press, New York, 1960.
5. W. Ehrenberg. Sci. Am. 217, 103, 1967.
6. R.D. Astumian, P.B. Chock, T.Y. Tsong, and H.V. Westerhof. Physical
Review A 39, 6416, 1989.
7. M.W.Ho. In Reassessing the Metaphysical foundations of Science
(W. Harman, and J. Clark, eds.), Institute of Noetic Sciences, San
8. M.W. Ho. The Rainbow and the Worm: The Physics of Organisms, World
Scientific, Singapore, 1993.
9. C.W.F. McClare. J. theor. Biol. 30, 1, 1971.
10. M.W. Ho and F.A. Popp. In Thinking About Biology (W.D. Stein
and F. Varela, eds.), Addison-Wesley, New York, 1993.
11. G.R. Fleming, J.L. Martin, and J. Berton. Nature 333, 190,
12. I. Gonda and B.F. Gray. In Biomolecular Structure, Conformation,
Function, and Evolution vol. 2, Pergamon, Oxford, 1980.
13. L.A. Blumenfeld. Physics of Bioenergetic Processes,
Springer-Verlag, Heidelberg, 1983.
14. G.R. Welch and D.B. Kell. In Fluctuating Enzyme (G.R. Welch,
ed.), p.451, John Wiley & Sons, New York, 1986.
15. L. Onsager, Phys. Rev. 37, 405; and 38,
16. K.G. Denbigh. The Thermodynamics of the Steady State,
Mathuen & Co., Ltd., New York, 1951.
17. H.J. Morowitz. Energy Flow in Biology, Academic Press, New
18. G.L. Sewell.In Large-Scale Molecular Systems: Quantum and
Stochastic Aspects (W. Gans, A. Blumen and A. Amann, eds.), p.1,
Plenum Press, New York, 1991.
19. H. Fröhlich, Adv. Electronics and Electron. Phys. 53,
20. T.M. Wu. In Bioelectromagnetism and Biocommunication (M.W.
Ho, F.A. Popp and U. Warnke, eds.). World Scientific, Singapore (in
21. N.G. Duffield. J. Phys. A: Math. Gen. 21, 625, 1988.
22. R. Lumry. In Protein-water Interactions (R.B. Gregory, ed.),
Marcel Dekker, New York, 1994.
23. M.W. Ho, F.A. Popp and U. Warnke eds. Bioelectrodynamics and
Biocommunication, World Scientific, Singapore (in press).
24. M. Galle, R. Neurohr, G. Altman, and W. Nagl, Experientia
47, 457, 1991.
25. M.W. Ho, X. Xu, S. Ross, and P.T. Saunders. In Recent Advances
in Biophoton Research (F.A. Popp, K.H. Li and Q. Gu, eds.), p 287,
World Scientific, Singapore, 1992.
26. G.R. Welch, Fluctuating Enzyme, John Wiley & Sons, New
27. M.W. Ho, T.A. Stone, I. Jerman, J. Bolton, H. Bolton, B.C. Goodwin,
P.T. Saunders, and F. Robertson. Physics in medicine and Biology
28. M.W. Ho, A.French, J. Haffegee, J. and P.T. Saunders. In
Bioelectrodynamics and Biocommunication (M.W. Ho, F.A. Popp, and U.
Warnke, eds.) , World Scientific, Singapore (in press).
29. M.W. Ho, and M. Lawrence, Microscopy and Analysis,
September, 26, 1993.
30. M.W. Ho, and P.T. Saunders. In Bioelectromagnetism and
Biocommunication (M.W. Ho, F.A. Popp and U. Warnke, eds.). World
Scientific, Singapore (in press).
31. I. Havel, I. Center for Theoretical Study Offprint, Praha,
32. A.J. Leggett, Proc. Int. Symp. Foundations of Quantum Mechanics,
Tokyo, p.74, Springer-Verlag, Berlin, 1983.
33. F.A. Popp. In Disequilibrium and Self-Organization (C.W.
Kilmister, ed.), p.207, Reidel, Dordrecht, 1986.
34. F.A. Popp, K.H. Li, and Q. Gu, eds. Recent Advances in Biophoton
Research, World Scientific, Singapore, 1992.
35. F.A. Popp and K.H. Li. In Recent Advances in Biophoton Research
(F.A. Popp, K.H. Li and Q. Gu, eds.), p. 47, World Scientific, Singapore,
36. R.J. Glauber. In Quantum Optics (R.J. Glauber, ed.),
Academic Press, New York, 1969.
37. F. Musumeci, M. Godlevski, F.A. Popp, and M.W. Ho. In Recent
Advances in Biophoton Research (F.A. Popp, K.H. Li and Q. Gu, eds.),
p. 327, World Scientific, Singapore, 1992.
38. P. Bak, P. In Thinking About Biology (W.d. Stein and F.J.
Varela, eds.), p. 255, Addison Wesley, New York, 1993.
39. C. Zhang, and F.A. Popp. In Bioelectromagnetism and
Biocommunication (M.W. Ho, F.A. Popp and U. Warnke, eds.). World
Scientific, Singapore (in press).