Work and Free Energy -- The Dance of LEP on LEC LO25369 -Part I

From: AM de Lange (
Date: 09/24/00

Dear Organlearners,

Greetings to you all.

I dedicate this contribution to all authentic learners. Try keep on
swimming vecause this river is going to flow very far.

I want you to imagine the following coin. When looking at the one side of
it, it has a picture one it. When turning it around to look at the other
side, it has a movie on that side which can never be frozen. Like
Heraclitus said more than two millennia ago: "panta rhei" (all flow). When
turning the coin around once more, it has again a picture on it. The
picture is in some aspects the same as the previous one, but in all the
other aspects it has changed with lesser or greater differences. The coin
can be turned over and over again. By doing so, we will observe at least
one of seven patterns. It is the pattern
      being to becoming to being to becoming to being to .....

This contribution is on that coin. This contribution will function as that
coin. Take a deep breath because you are about to turn the coin from the
present picture to the coming movie on the other side. At the end of this
contribution we will again turn the coin around to see the end picture. (I
will not use any subheadings which will freeze the movie.) Later you may
study the contribution again, i.e turning the coin around to experience
"panta rhei" once again. The beginning picture then will be different to
the beginning picture now. The end picture then will be different to the
ending picture of this session. It is because you will be exploring deeper
and deeper into creativity with every full revolution of the coin.

Turn the coin now.

Some people want to work and others not. Some have to work and others not.
Some work good and others not. Whatever the case, all people have some
stance in work, all think about work and all are affected by work. So what
is work?

Work has many facets or qualities in its form. These facets are covered by
a variety of subjects like theology, law, sociology, economics and
politics. These facets point to form within form, in other words,
"patterns in form". But work has also content which is studied in subjects
like physics and chemistry. It is because of this content that work can be
quantitatively determined and thus be called a physico-chemical quantity.

When we think of anything which has content and form, we tend to focus on
one of them and not both. Thus we do not become aware of the interplay
between content and form. Form influences content. For example, a cube
and a sphere have different forms. Consider a sphere with diameter of 1
meter which fits tightly into a cube with sides of 1 meter. Their contents
(volumes) differ. Likewise does content influence form. For example, as
animals become more massive (content), their legs become progressively
thicker (form) than their body. The legs of an antelope are dainty
compared to the legs of an elephant.

The work done on anything changes the form of that thing, externally or
internally. It is as if the work gets "frozen" into the new "patterns in
form" of that thing. We are invited to think that the work changes the
"organisation" of that thing. Since we are concerned about our human
organisations and how to change them for the better, it will do us good to
bear in mind that work is essential to such organisational changes.

How is it possible at all that work changes the "patterns in form"
(organisation) of anything?

How much of an answer will we get from the physicist?

When a physicist has to describe such an organisational change, he would,
for example, say that the work will move a weight from a lower to a higher
height. It is perhaps such an unpoetic description of organisational
change that we may not even recognise it as one. Nevertheless, the very
description which the physicist uses to calculate work is
. force (weight) x distance (increase in height)
This "pattern in form" consists of three things, one quantity (force),
another quantity (displacement) and multiplication (operation). The
measurement of distance is something which humankind are able
to do for many millennia. The measurement of force became possible
only after Newton had formulated his famous laws of mechanics,
thus making it possible to identify force.

The physicist can measure the force directly and can also measure the
distance directly, but has no instrument at all to measure the work
directly. Thus the physicist has to use the "description" of work to
calculate it in terms of measured force and measured distance. In other
words, the physicist has to use the fact that work changes the "pattern in
form" (or organisation) of something. To make use of a fact is not the
same as explaining a fact. Thus it seems as if humankind's many millennia
old capacity to measure distance and its three centuries old capacity to
measure force (based on Newtonian mechanics) cannot help us to explain why
work changes the "pattern in form" of anything.

But Newton's own work did something most important which we seldom bear in
mind. It caused a change in the organisation of the minds of other
physicists. He fired their imagination to seek other laws besides his own
mechanical laws. One by one they discovered these other laws too. It is
even more astounding that they could apply the "description" of work to
situations in which these other laws were operating. Consequently, the
fact that work changes the "pattern in form" (or organisation) of anything
was very useful to them. Yet they very seldom articulated this fact in
words, although they continually articulated it in their symbolic

Gradually they became aware that there was some quantity which has many
forms (mechanical, elastical, gravitational, electrical, magnetical, etc.)
with laws operating in each form and that work could be used to connect to
each of its many forms. This quantity became known as energy. Its content
is expressed in the same unit as work. The content of each of its many
forms is also expressed in the same unit. The unit for energy in the SI
(System International) is the "joule", symbol "J". Other units are the
erg, calorie, foot-pound, etc.

As is the case for work, no instrument exists by which any these
many forms of energy can be measured directly. Any quantitative
value of every form of energy has to be determined based on
. * measurements of at least two quantities as indicated
. by "description",
. * calculation based on the "description" of that form of
. energy involving the quantities.
In each of these "descriptions" a "pattern in form" of energy is used,
prescribed by the laws discovered for that form of energy. In other
words, all the quantitative work of physicists on the many forms
of energy depends on the "patterns in form" (or "organisation") of
energy which could be changed by work.

The modern technological world runs on fossil fuel, especially oil, as its
source of energy. This oil is measured in "barrels". The "barrel" is a
unit of volume in the oil industry. Its volume is some 200 litres. The
"barrel" does not measure the amount of energy, whatever the form, within
that oil. The oil barons assume that for the oil its "volume is linearly
proportional to" its chemical form of energy. Thus even they make use of a
"pattern in form", namely "volume is linearly proportional to".

Eventually physicists became very excited because it seemed that this very
quantity energy with its many forms had a law of its own. Their excitement
stemmed from the fact that this law seemed to be indifferent to the
existence of the many other laws, almost as if it was far more superior
(or fundamental) to all these other laws so as not to be influenced by any
of them. It was as if this law was blind to the "pattern in form" of
energy, even though physicists had to make repeatedly use of "pattern in
form" to get the idea for this law and eventually to verify their idea.
It is now usually called the Law of Energy Conservation (LEC). It is often
also called the First Law of Thermodynamics, but this is somewhat a
misnomer as we will soon see.

The formulation of LEC in symbols is very simple. Consider any system
symbolised by SY which is in contact with many other systems. Consider all
these other systems together as the surrounding system (or environment or
context) symbolised by SU. The system SY and the surrounding system SU
form together the encompassing system called the universe and symbolised
by UN. Let E(un) be the total energy of the universe. This total energy
consists of all forms of energy, i.e. not one form ever excluded, not even
nuclear energy. LEC says that the total energy E(un) of the universe is
constant, i.e.
. E(un) = constant (first form)

This equation can be expanded easily into three other equations for energy
which employ the strange symbol /_\ for "difference" or "increment". (It
is the best approximation of the Greek capital letter "delta".) Firstly,
let E(un, 1) be the value of total energy E of the universe at a time
t(1). Let E(un, 2) be its value at a later time t(2). Then
. E(un, 1) = constant
. E(un, 2) = constant
By subtracting the first equation from the second, we get
. E(un, 2) - E(un, 1) = 0
This difference may be written concisely as
. /_\E(un) = 0 (second form)
It says that as time goes on, there is no difference in the total
energy E of the universe. This total energy of the universe cannot
increase (be constructed) nor decrease (be destroyed). The total
energy E of the universe cannot change.

Let the total energy of the system be E(sy) and that of the surroundings
be E(su). When they are added, their energies cannot both increase or both
decrease. In other words, they must add up to the total energy E(un) of
the universe which is constant. Hence we have
. E(sy) + E(su) = E(un) = constant (third form)

Let the value of the system's total energy be E(sy, 1) at time t(1) and
E(sy, 2) at time t(2). Let the value of the surrounding's total energy be
E(su, 1) at time t(1) and E(su, 2) at time t(2). Then at times t(1) and
t(2) for the universe we have
. E(sy, 1) + E(su, 1) = constant
. E(sy, 2) + E(su, 2) = constant
By subtracting the first equation from the second, we get
. E(sy, 2) - E(sy, 1) + E(su, 2) - E(su, 1) = 0
This difference may be concisely written as
. /_\E(sy) + /_\E(su) = 0 (fourth form)
where, for example,
. /_\E(sy) = E(sy, 2) - E(sy, 1)

Please take care that you do not read in this fourth equation something
such as
. /_\E(sy) = 0 AND /_\E(su) = 0
For all changes, only for the universe itself will
. /_\E(un) = 0
It will usually happen that the system's total energy /_\E(sy)
will increase or decrease rather than remain constant. Assume
that it increase (positive sign) by +5J. Then
. +5J + /_\E(su) = 0
so that /_\E(su) has to be -5J. In other words, an INcrease
(like +5J) in the system's total energy will be balanced by a
DEcrease of the same magnitude in the surrounding's total energy.
What the one system wins, the other system must lose. Both the
system SY and its surroundings SU cannot be winners.

What a strange world the physicists were living in! All the formulations
of all the laws which they have discovered were equations which made use
of the sign "=". Even their "descriptions" of work for each form of
energy made use of it. So much equality everywhere -- the physicist's
reality of equalities was the politician's dream. Yet for the system SY
and its surroundings SU and as a result of changes, only one can be the
winner in total energy E through this very equivalence relationship.

But the reality of the physicists soon became their nightmare. About a
dozen years after the discovery of LEC, Rudolf Clausius made a strange
discovery when following up the work of Sidi Carnot. He played with a
description having the pattern
. heat-flow / temperature
Compare it with the pattern
. force x distance
for work. It uses division "/" whereas work uses multiplication
"x", its complementary dual. Whereas the work changes the
energy E of a system so that /_\E may be measured and
calculated in terms of a "force x distance" description, he
assumed that the pattern "heat-flow / temperature" will allow
one to measure and calculate the change /_\S in a quantity
which he called entropy S. Thus this entropy S had to be the
complement (not equal) of energy E.

By simple though experiments (see Primer on Entropy)
< >
< >
< >
< >
< >
< >
he was able to conceptualise something which we may express
in the trend of the following. (We will use the sign "<>" to mean
"is not equal to", the sign ">" to mean "is greater than" and the
sign "<" to mean "is smaller than".)

The Law of Entropy Production (LEP):
. S(un) <> constant (first form)
. /_\S(un) > 0 (second form)
. S(sy) + S(su) <> constant (third form)
. /_\S(sy) + /_\S(su) > 0 (fourth form).
Compare its stunning complementarity (not equality!) with the
Law of Energy Conservation (LEC).
. E(un) = constant (first form)
. /_\E(un) = 0 (second form)
. E(sy) + E(su) = constant (third form)
. /_\E(sy) + /_\E(su) = 0 (fourth form)

The first form says that the entropy S of the universe UN is never
constant. The second form says that the entropy of the universe UN is
always increasing. The third form says that the sum of the entropies of
both the system SY and the surroundings SU are never constant. The fourth
form says that the sum of the changes of the entropies of the system SY
and the surroundings SU is always increasing.

Here physicists had their first ever law which did not make use of the
"equivalence relationship = of being", but rather the "order relationship
> of becoming". It stunned them. Here is one of many reasons. (The unit of
entropy is "J/K" or "joule per kelvin".) Let the change in entropy
/_\S(sy) of the system be the increase +4J/K. Then we have
. +4J/K + /_\S(su) > 0
Should we have had the equality
. +4J/K + /_\S(su) = 0
then ONE and only ONE value is possible for /_\S(su), namely
the decrease -4J/K. But "should" is one thing and "must" is another
thing. Experiments tell us that we must have the ordering
. +4J/K + /_\S(su) > 0
so that uncountably MANY values are possible for /_\S(su). Here
are, for example, six possible cases:
. +4J/K + (-3J/K) > 0
. +4J/K + (-2J/K) > 0
. +4J/K + (-1J/K) > 0
. +4J/K + (-0J/K) > 0
. +4J/K + (+1J/K) > 0
. +4J/K + (+2J/K) > 0
Do observe that in the first four cases only the system SY is the
winner in entropy S, but in the last two cases also the surroundings
SU is a winner. Whereas the "=" affords us a "one-to-one-mapping",
the ">" affords us a "one-to-many-mapping".

All races seems to have one winner for each race. But there is one
exception -- the yearly great Comrades Marathon of South Africa. You will
not comprehend it unless you have seen a rich video on this race in which
more than 20 000 runners participate. Each runner who completes this
gruelling race against the self is a winner with time as the referee.

What? A new world in which equality for entropy S does not exist so that
sometimes both the system SY and the surrounding SU can be winners? Then
rather the old world of equality for all the other laws including energy
so that only one system, either SY or SU, but not both, can be the winner.
The Law of the Excluded Middle (LEM) of logic helped physicists so nicely
to discover all their famous physical laws. How can they scrap LEM for
such an infamous thing as LEP. No dice. This will make their world too

So they invented a discipline which they called thermodynamics, but which
they rather should have called thermostatics. In this discipline they
forced all work and thus changes of energy to become "reversible". In that
case (putting a = on either side of <> and either side of >)
. S(un) =<>= constant (first form)
. /_\S(un) =>= 0 (second form)
. S(sy) + S(su) =<>= constant (third form)
. /_\S(sy) + /_\S(su) =>= 0 (fourth form)
where the hideous signs "=<>=" and "=>=" means "almost equal
with negligible discrepancy". In other words, for perfectly reversible
processes or changes they would have (removing the <> and the >
and one of the =)
. S(un) = constant (first form)
. /_\S(un) = 0 (second form)
. S(sy) + S(su) = constant (third form)
. /_\S(sy) + /_\S(su) = 0 (fourth form)
and thus would have regained their world of equalities in which
only one system can be the winner and LEM dictate the rest.
LEP has become like LEC.

Before this "reversibilisation" took place in the mind of the far majority
of physicists as well as engineers who followed their example, almost
every authentic thinker in physics had his own interpretation for entropy.
For example, Clausius interpreted it as "maximisation", Boltzmann as
"probability", Planck as "propensity" and Eddington as "time's arrow".
But eventually almost everybody began to bow before the interpretation
that entropy is a measure of "chaos". Yes, in the world of equalities in
which only one system can be the winner, truth is what you want it to be
and LEM dictates the rest, confusion (chaos ;-) must increase.

How can processes be made reversible as "classical thermodynamics"
(thermostatics) requires? Newton's Third Law of mechanics says that for
every action there is an equal, but opposite reaction. So, take the que
given more than three centuries ago and let the temperatures T(sy) of the
system SY and T(su) of the surroundings SU differ only by an infinitesimal
amount. Then, as heat Q flows from SY to SU, the change in entropy will be
. -Q/T(sy) + Q/T(su)
But since
. T(sy) =>= T(su)
which is intended to be in "perfect reversibility"
. T(sy) = T(su) = T (common temperature)
the expression
. -Q/T(sy) + Q/T(su)
. -Q/T + Q/T
which is equal to zero.

The only trouble is that for heat Q to flow "reversible" from SY to SU (or
vice versa) where the difference in temperature is almost zero, i.e. T(sy)
=>= T(su), it takes a very, very long time for all the heat Q to get
transferred! This is the reason why "classical thermodynamics" ought to
be called "thermostatics". This is also the reason why I prefer to speak
of LEC and LEP rather than the "first law of thermodynamics" and the
"second law of thermodynamics". The "second law of thermodynamics" is
merely a curiosity which had been phased out by way of forcing all
changes/processes to become "reversible". The remainder was then enshrined
by chaos.

Look at the temperature T of thermal energy in the "description" of
entropy. It is an intensive quantity (see Primer on Entropy what
"intensive" means). But is the temperature T of thermal energy the only
intensive quantity which a system may have? Applying LEM, yes, but
suspending LEM, no. The intensive quantity for pneumatic energy is the
pressure P, for electrical energy it is the electrical potential V, for
elastical energy it is the elastic tension T, etc. So what happens when we
apply the formula
. "reversible action = reaction"
to the flow of any other form of energy between the system SY
and surroundings SU?

Consider the flow of pneumatic energy which is called pneumatic (or PxV)
work. Here P is the symbol for pressure and V the symbol for volume. Now
consider the "becoming pattern" (see the series on the topic "To become or
not to become")
. [P(sy) - P(su)] x /_\V
where /_\V is the volume flowing from pressure P(sy) in the system
to pressure P(su) in the surroundings, or vice versa. Applying the
"reversible action = reaction" formula here means
. P(sy) = P(su)
so that
. [P(sy) - P(su)] x /_\V = 0.
Thus we can say with a nice equality that the pneumatic work
P(sy) x /_\V which enters the system SY is the pneumatic work
P(su) x /_\V which leaves the surroundings SU. But when we drop
the "reversible action = reaction" formula so that
. P(sy) <> P(su)
the expression
. [P(sy) - P(su)] x /_\V
is not zero anymore. What does it represent?

In the "idyllic reversible" world in which equality occurs everywhere,
one system wins and LEM reigns, this expression does not make
sense. The only expression which do make infinitesimal small
sense in this "idyllic reversible" world is
. -Q/T(sy) + Q/T(su)
or also written as
. [1/T(su) - 1/T(sy)] x Q
which tell us that entropy is increasing. To go beyond this infinitesimal
small sense we will have to know what entropy is. This soon becomes a
nightmare because the interpretation of entropy as "chaos" which has won
in this "idyllic reversible" world. With "chaos" as the interpretation,
the positive increase of the expression
. [1/T(su) - 1/T(sy)] x Q
tells us that one day the universe will end in a white hot hell like in
the beginning with the Big Bang. In other words, all evolution is a mere
illusion, even God Creator is an illusion.

In the "real irreversible" world the expression
. [P(sy) - P(su)] x /_\V
is yet another way of producing entropy! The actual entropy which it
will produce is equal to
. [P(sy)/T(sy) - P(su)/T(su)] x /_\V
It is difficult to stick to the "chaos" interpretation of the "idyllic
world" in this expression of the "real irreversible" world. When we add
all similar expressions for each form of energy together, we will get the
whole of "entropy production". To interpret this "whole of becoming
patterns" with "chaos" as candidate is perhaps the worst bet we could have
made upon a possible winner! In this "real reversible" world there are
more than one winners so that even betting becomes a farce!

The best interpretation which I can give for the whole of adding together
all "becoming patterns" of the form
. difference x flow
. (1/T(sy) - 1/T(su)) x Q
. [P(sy)/T(sy) - P(su)/T(su)] x /_\V
is the following:
. "patterns in form", or for short, "organisation".
Prigogine gives the impression (but do not actually make such a claim)
that entropy is a measure of "chaos and order". It is easy to show
(See Primer on Entropy) that entropy also measures order. But who
knows of any "organisation" without "chaos and order"? So let us go
one step further and combine "chaos and order" into "organisation".
Consequently we assume that entropy is indeed a measure of

The findings in the "idyllic reversible world" were not all in vain.
Perhaps the most important insight form this world is that when entropy is
transferred reversibly, what the system SY wins (respectively loses) in
entropy, the surroundings SU loses (resp wins) in entropy. Furthermore,
this transfer of entropy S is not independent of the transfer of total
energy E, but rather tightly associated with it. Consider any process
(reversible or irreversible) for which the transfer in total energy is,
for example:
. /_\E(sy) + /_\E(su) = 0
. (-5J) + (+5J) = 0
. 0J = 0
The system SY loses (- sign) and the surroundings SU wins (+ sign)
5J of energy. Should this process be reversible, the transfer in
entropy would be something such as: (Please note that reversible
imply the = rather than the >)
. /_\S(sy) + /_\S(su) = 0
. (-4J/K) + (+4J/K) = 0
. 0J/K = 0
Here the system SY loses and the surroundings SU wins 4J/K of
entropy. It follows the same pattern as energy, only with different
units and magnitudes.

However, should the process be irreversible, yet beginning and
ending at the same states as the reversible process, the outcomes
for entropy would be something like the following: (Please note that
irreversible imply the > rather than the =)
. /_\S(sy) + /_\S(su) > 0
. (-4J/K + 1J/K) + (+4J/K +2J/K) > 0
. (-3J/K) + (+6J/K) > 0
. +3J/K > 0
Here again the -4J/K to +4J/K is the transfer in entropy as in the
reversible case. But now the +1J/K is the extra entropy produced
in the system SY and the +2J/K is the extra entropy produced in
the surroundings SU. The total change of entropy in the system SY,
namely -3J/K, is such that it hides its two components
-4J/K(reversible) and +1J/K(irreversible). The same goes for the
surroundings SU. This means that there is no such a thing as
transparency all the way! Consequently, when we compare the final
outcomes of LEC and LEP for the irreversible case, namely
. /_\E(sy) + /_\E(su) = 0
. (-5J) + (+5J) = 0
. /_\S(sy) + /_\S(su) > 0
. (-3J/K) + (+6J/K) > 0
we are lured into making the fatal conclusion that LEC and LEP
act independently from each other since (-5J) + (+5J) = 0 appears
to be symmetrical while there is no symmetry in (-3J/K) + (+6J/K) > 0.

I say "fatal conclusion" because often people in the "real irreversible"
world will tend to take energy in account, but only seldom will they think
of entropy too. These people do not know that LEC and LEP are
complementary duals which should never be severed. Yes, it is extremely
difficult to picture complementary duals in numerical examples such as
. (-5J) + (+5J) = 0,
. (-3J/K) + (+6J/K) > 0
But it is even easier to make the following graver mistake.

[Here Part I ends. This break is due to technology and not because the
coin has been turned back. The movie is still running!]

Take care!

At de Lange <>
Snailmail: A M de Lange
Gold Fields Computer Centre
Faculty of Science - University of Pretoria
Pretoria 0001 - Rep of South Africa


"AM de Lange" <>

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