Replying to LO25369 --
Greetings LOers!
Dear At,
Thanks so much for your contribution. It freed up a logjam in my mind
with which I have been wrestling for some 6-8 months. At least, I think
it did. I have some comments on your contribution that I am articulating
for you and others to scrutinize to make sure that I am thinking along the
right path. This whole contribution, although written as if I have a
perfect understanding (this was the most comfortable style of writing for
me as I simultaneously wrote and thought over the past month since At
wrote his post), is actually one long question - me trying to find out if
I understand all of this "stuff" correctly. I welcome input, corrections,
and observations from anyone. A note on the content to fellow LO readers
- I use many of the symbols that are commonly used by At. This is largely
a conceptual post, with relatively little translation into the practical
realm. As a result, reading it may or may not be the best use of your
time.
In your contribution you articulated the following relationships:
The Law of Energy Conservation (LEC) in a number of forms:
(1) E(un) = constant (The total energy (E) of the universe (un) is
constant)
(2) /_\E(un) = 0 (The total energy of the universe can neither increase
or decrease - the change (/_\) in the total energy of the universe over
time equals zero)
(3) E(sy) + E(su) = E(un) = 0 (Restates the second form, but divides the
universe into a particular system of interest (sy) and its surroundings
(su), or everything else in the universe)
(4) /_\E(sy) + /_\E(su) = 0 (The exchanges of energy between a system and
its surroundings, constrained by the LEC, are a zero-sum game - what one
loses, the other must gain)
The Law of Entropy Production (LEP) in a number of forms, paralleling the
forms of the LEC spelled out above, but emphasizing that, while the LEC in
all forms represents a universal equivalence relation, the LEP represents
a universal order relation:
(1) S(un) <> constant (The total entropy (S) of the universe is NOT
constant)
(2) /_\S(un) > 0 (The total change in the entropy of the universe over
time is greater than zero - the entropy of the universe is increasing
towards a maximum)
(3) S(sy) + S(su) <> constant (this partials out S(un) into two parts
such that S(sy) + S(su) = S(un), then restates the first form. The sum of
the entropy of a system and the entropy of its surroundings is not
constant)
(4) /_\S(sy) + S(su) > 0 (the sum of the changes in the entropy of a
system and the changes in the entropy of its surroundings over time is
greater than zero - is always increasing towards a maximum)
Eventually, At related the quantity Energy with the quantity Entropy using
the work of J W Gibbs, showing that, while there is no exact equivalence
relationship between these two quantities, they are indeed closely related
through the concept of "free energy".
F = E - T x S (Free energy (F) equals the total energy (E) minus the
absolute temperature (T - measured on the Kelvin scale) multiplied by the
entropy (S))
F(un) = E(un) - T(un) x S(un)
F(sy) = E(sy) - T(sy) x S(sy)
F(su) = E(su) - T(su) x S(su)
Then, At showed a lawful, universal order relation that must be true for
Free Energy (F) using the following algebraic manipulation:
snip
>. /_\E(un) = 0
>. /_\S(un) > 0
>Should we want to bring in the system SY, then we must bring in
>also the surroundings SU so as not to lose wholeness on E and S.
>This will result in
>. /_\E(sy) + /_\E(su) = 0
>. /_\S(sy) + /_\S(su) > 0
>Let us now begine with LEP and apply
>. F = E - T x S
>as
>. S = (E - F) / T
>to it. It will result into:
>. /_\[(E - F) / T)](sy) + /_\[(E - F) / T](su) > 0
>rearranged into:
>. [/_\E(sy) + /_\E(su)] - [/_\(F/T)(sy) + /_\(F/T)(su)] > 0
>which collapses with LEC into the remainder
>. - [/_\(F/T)(sy) + /_\(F/T)(su)] > 0
>This expression can then be inverted as
>. /_\(F/T)(sy) + /_\(F/T)(su)] < 0
>Since we know that T(sy) > 0 and T(su) > 0 (an absolute temperature T
>is always positive) we may conclude the following.
>. /_\F(sy) + /_\F(su) < 0
>Let us not forget that this expression emerged as a new whole from the
>combination of LEC and LEP as two wholes. It is the "whole of both
>LEC and LEP".
>
>Let us compare this "whole of both LEC and LEP"
>. /_\F(sy) +/_\F(su) < 0
>with LEC and LEP individually as
>. /_\E(sy) + /_\E(su) = 0
>. /_\S(sy) + /_\S(su) > 0
>Firstly, this "universal order relathionship for free energy" tells us that
>the free energy F is NOT CONSERVED like the total energy E, NOR MAXIMISED
>like the entropy S. It is as if the free energy F is behaving in a manner
>opposite to entropy S. The free energy F of the universe is decreasing
>continuously as the universe is becoming more organised. In fact, we will
>use the very expression
>. /_\F(sy) = /_\F(su) = 0
>taken together into
>. /_\F(un) < 0
>as our very principal definition for the SPONTANEOUS organising of
>the universe UN....
end snip
So we have our 3 universal relationships (one equivalence and two order
relationships) articulated as follows:
(1) E(un) = constant
(2) /_\E(un) = 0
(3) E(sy) + E(su) = E(un) = constant
(4) /_\E(sy) + /_\E(su) = 0
(1) S(un) <> constant
(2) /_\S(un) > 0
(3) S(sy) + S(su) = S(un) <> constant
(4) /_\S(sy) + /_\S(su) > 0
(1) F(un) <> constant
(2) /_\F(un) < 0
(3) F(sy) + F(su) = F(un) <> constant
(4) /_\F(sy) + /_\F(su) < 0
To summarize the relationship between these three quantities:
Energy forms the content of all things (objects and systems, static and
dynamic), and the total energy in the universe is constant.
Entropy is a measure of the organization of the energy, while a change in
the entropy of a system of energy over time is an indication of a change
in organization, or an evolution of the system.
At least a portion of the energy in a system is tied up in maintaining
the organization of that system and is therefore not available for
performing work on the system and changing its organization. Once this
energy has been accounted for, any remaining energy is Free Energy - that
portion which may be harnessed to perform work - either work on its
surroundings or work required to change the organization, or entropy, of
the system itself.
This is the relationship that is captured by Gibbs in the formula
(solving, in turn, for each of the 3 quantities mentioned above):
E = F + T x S
S = (E - F) / T
F = E - T x S
The change in entropy for the universe, according to the LEP, must always
be to INCREASE. Inversely (and necessarily, due to the fact that the
total energy in the universe is constant, and as entropy increases, more
of the total energy of the universe is tied up in maintaining this
increasing organization), the free energy of the universe must always
DECREASE as the entropy of the universe increases. At the point where the
free energy of the universe is exhausted, the entropy of the universe will
also reach its maximum level. Changes will no longer occur and the
universe will become stagnant. However, while the entropy of the universe
is increasing and while free energy is being consumed, the universe is
changing/evolving spontaneously (using its own free energy to affect the
changes in its own organization). Free energy, then, is the portion of
energy that fuels the entropy production, and hence all changes, in the
universe.
The law governing the conservation of energy is absolute for the entire
universe, but not for any open system within the universe in particular.
A system may gain or lose energy as it changes organization (/_\E(sy) <> 0
- but its surroundings must lose or gain an equivalent amount of energy).
Similarly, the law that necessitates that the free energy of the universe
must decrease and the entropy of the universe must increase also doesn't
necessarily hold for any open system within the universe. Any given
system may increase in free energy or decrease in entropy (/_\F(sy) <> 0,
/_\S(sy) <> 0 - but the net exchange when these changes are considered
within the context of the universe must be for free energy to decrease and
entropy to increase overall).
However, it is still true that if the free energy in the system is
decreasing (/_\F(sy) < 0), the system is acting spontaneously. The
complexity of the organization of a system of energy is contingently and
directly related to the rate at which entropy is being produced (although
not solely dependent on this). And, if a system is acting spontaneously
and is producing entropy at a sufficient rate, it may potentially reach a
bifurcation point followed by the spontaneous, self-organization of a
level of higher complexity (for example, emerging to a more effective
learning organization). For these reasons, it becomes important to
consider for individual systems whether or not the system is acting
spontaneously or is being driven in a non-spontaneous manner (/_\F(sy) >
0).
In order to keep our eye on the whole of the changes in energy, entropy
and free energy, we need to track, not just the changes to the system
itself as a function of the dissipation of free energy and entropy
production, but the interaction of the system with its surroundings.
Expressed in terms of free energy, this is represented by the fourth form
of the law of the reduction in free energy (my term) that At delineated:
/_\F(sy) + /_\F(su) < 0.
Before we look at the first term (/_\F(sy)) any further, I wanted to make
a few comments regarding the second term (/_\F(su)). As I understand the
way that At articulated it, the interaction of the system with its
surroundings can be interpreted as either work done by the system on its
surroundings, or work done on the system by its surroundings. It
represents the "reversible" flow of energy (the portion of the change in
free energy that is conserved and and might be reversed or reconverted
back into its original form). If the system is performing work on the
surroundings, /_\F(su) will be a net gain. If the surroundings are
performing work on the system, /_\F(su) will be a net loss (negative
value). We might, therefore, choose to partial /_\F(su) into the
following equation:
/_\F(su) = /_\F(SUin) - /_\F(SUout)
where /_\F(SUin) is equal to the amount of free energy flowing into the
surroundings from the system of interest and /_\F(SUout) is equal to the
amount of free energy flowing out of the environment into the same system.
At expressed one understanding of /_\F(su) as follows:
/_\F(su) = -W
Here, we are essentially viewing the change in free energy from the
perspective of the surroundings and viewing work from the perspective of
the system. We might, therefore choose to write this equation as:
/_\F(su) = -W(sy)
to show that the change in the free energy of the surroundings is equal to
opposite of the net work done on the surroundings by the system. If work
is flowing out of the system and into the surroundings, W will have a
negative value and /_\F(su) will have a positive value (e.g., W(sy) = -8J,
so /_\F(su) = -W = -(-8J) = 8J). If work is flowing into the system from
the surroundings, W will have a positive value and /_\F(su) will have a
negative value showing that free energy is leaving the surroundings in
order to perform the work on the system (W(sy) = +8J, so /_\F(su) = -W =
-(+8J) = -8J).
Returning, now, to the term /_\F(sy), we can also state a clear and lawful
relationship between it and work (W) as At did for us:
snip...
>...Take the work equation above
>. /_\F(su) = -W
>and substitute it in the "universal order relationship for free
>energy"
>. /_\F(sy) + /_\F(su) < 0
>which will then result into
>. /_\F(sy) - W < 0
>or rearranging
>. /_\F(sy) < W
>When W has a positive value, it means that some energy enters the system
>SY through work DONE ON the system. Hence F(sy) increases so that
>/_\F(sy) is positive. But when W has a negative value, it means that
>energy leaves the system through work DONE BY the system on the
>surroundings. Hence F(sy) decreases so that /_\F(sy) is negative. In other
>words, what goes in raises with a positive difference whereas what goes
>out lowers with a negative difference. This is the bookkeeping which I
>have mentioned.
end snip
How can we understand this in yet another way? We can inform it by
looking at some of the work of Ilya Prigogine, the nobel prize winning
thermodynamicist responsible for many of the concepts around the
importance of entropy production and its link to the ever-increasing
complexity that we observe around us whom At has mentioned numerous times.
In his book with Isabelle Stengers, Order out of chaos, he states that
when we consider the change in entropy (S) within a system over an
interval of time, we can partial out the total change into two, mutually
exclusive portions, (1) the portion attributed to the entropy production
resulting from IRREVERSIBLE (i) processes within the system - the
dissipation of free energy - which we will call /_\S(i), and (2) the
"reversible" EXCHANGES (e), or flow, of entropy/free energy between the
system and its surroundings - which we will call /_\S(e).
/_\S(sy) = /_\S(i) + /_\S(e)
Prigogine used this equation to define various states of organization for
an open system. First, he described a system at maximum entropy where no
changes are happening - the state of stable equilibrium. In this
situation, /_\S(sy) = /_\S(i) + /_\S(e) = 0 with /_\S(i) = 0 and /_\S(e) =
0. There is no thermodynamic/entropic force acting within the system, and
therefore, no flow of energy.
Second, he described a second equilibrium state that he termed a dynamic
equilibrium state. This state is synonomous with the labile equilibrium
that At has described. In this state, the system has achieved a steady,
unchanging organization, but energy is still flowing through the system.
So, we have /_\S(sy) = /_\S(i) + /_\S(e) = 0, but /_\S(i) > 0 and /_\S(e)
<> 0, and /_\S(i) = -/_\S(e). This essentially tells us that the rate
that entropy is produced (increasing) within the system is cancelled out
by the rate that entropy is flowing out of the system (hence the negative
sign for /_\S(e), showing that the net exchange of entropy between the
system and its surroundings is a loss of entropy for the system). This
state is characterized by the minimum entropy production (and therefore,
the maxiumum efficiency) consistent with the constraints upon the system
(boundary constraints for incoming and outgoing energy flow and rate at
which energy is flowing through the system). !! However, it is crucial to
note that, while the system is not changing (/_\S(sy) = 0) and is
therefore in a state of equilibrium (albeit a dynamic or labile state),
there IS a constant/nondiminishing entropic force acting on/within the
system, and a const ant/nondiminishing flow of energy through the system.
Finally, Prigogine used this equation to define the system that was not at
equilibrium, paying special attention to systems that were far from
equilibrium (this is where bifurcations and spontaneous emergence into
organizations of higher complexity can occur). This would be represented
by /_\S(sy) = /_\S(i) + /_\S(e) <> 0, with /_\S(i) > 0, /_\S(e) <> 0, and
/_\S(i) <> /_\S(e). This distance from equilibrium, in Prigogine's
discussion, is an indicator of the "liveness" (to borrow a term from At's
essentialities) of the system. Near equilibrium, in what Prigogine termed
the linear realm (for which, for example, Onsager's reciprocal relations
are valid), a system not at equilibrium will spontaneously converge on an
equilibrium state (either that of maximum entropy for a closed/isolated
system, or minimal entropy production for an open system). Farther from
equilibrium, the system will emerge into the infamous "chaotic" state
where it will no longer converge on any equilibrium state - it remains
continually "alive" and changing.
If we were considering the total change in entropy for the universe, or
any isolated system, there would be no EXCHANGES between the system and
its surroundings, no flow of entropy, so
/_\S(e) = 0
and
/_\S(sy) and /_\S(i) would therefore all be equivalent terms. Given the LEP, we also know that, if there is any change in the entropy of the system, this term must be positive, so
/_\S(sy) = /_\S(i)) > 0
Stated in sentence form, the irreversible change in entropy due to entropy
production within the system must be positive. Here, the increasing
entropy of the system corresponds to the spontaneous evolution of the
system.
We have no such constraint on the reversible exchanges, or flow, of
entropy between an open system and its surroundings. This may be positive
or negative. This term, /_\S(e), is merely the opposite of the term
/_\S(su) that we have used in the fourth form of the LEP given above - the
same exchange of entropy between the system and its surroundings viewed
from the perspective of the system rather than the surroundings. When
/_\S(su) is positive, showing that the surroundings are gaining entropy in
the exchanges with they system, /_\S(e) is negative, showing that entropy
is flowing out of the system to produce the gaining entropy in the
surroundings.:
/_\S(sy) + /_\S(su) > 0
/_\S(sy) + [/_\S(su) = -/_\S(e)] > 0
/_\S(sy) + (-/_\S(e)) > 0
We can then plug our partialled equation for /_\S(sy) (thanks to Ilya) and
insert it into our fourth form of the LEP and see in another way that, of
course, it must be true:
[/_\S(sy) = /_\S(i) +/_\S(e)] +[/_\S(su) = -/_\S(e)] > 0
(/_\S(i) +/_\S(e)) + -/_\S(e) > 0
The two /_\S(e) terms cancel out, leaving
/_\S(i) > 0
When energy is dissipated irreversibly, it MUST result in an increase in
entropy. What we have done that adds to our understanding is illustrate
that the two terms in our fourth expression of the LEP are not independent
terms, but rather overlap with the common, reversible exchanges between a
system and its surroundings.
We can run through this same exercise, now, for free energy (F), similarly
enhancing our understanding. First, we will partial out the /_\F(sy) term
into the changes in free energy corresponding to the irreversible
dissipation of free energy in the entropy production of the system
(/_\F(i)) and the changes in free energy corresponding to the reversible
exchanges of free energy between the system and its surroundings (/_\F(e))
in the following equation:
/_\F(sy) = /_\F(i) + /_\F(e)
We also know from our exercise with the changes in entropy above that the
second term, /_\F(e), is the opposite of the /_\F(su) term in the fourth
expression in our "law of the dissipation of free energy", which we have
also shown to be the opposite of work (W - which we also wrote as W(sy) in
maintaining our holistic perspective of the universe), so
/_\F(e) = W = -/_\F(su)
or
/_\F(su) = -W = -/_\F(e)
Incidentally, this term, however it is represented, is indicative of the
coevolution of the system with its its environment.
Briefly revisiting our alternative equation for /_\F(su) stated above
/_\F(su) = /_\F(SUin) - /_\F(SUout)
we may also state an equivalent equation for /_\F(e):
/_\F(e) = /_\F(Ein) - /_\F(Eout)
where /_\F(Ein) is equal to the amount of Exchanged free energy (E)
flowing INto the system and the equivalent of /_\F(SUout), and /_\F(Eout)
is equal to the amount of Exchanged free energy flowing OUT of the system
and the equivalent of /_\F(SUin).
Finishing it off,
[/_\F(sy) = /_\F(i) +/_\F(e)] +[/_\F(su) = -/_\F(e)] < 0
(/_\F(i) +/_\F(e)) + -/_\F(e) < 0
The two /_\F(e) terms cancel out, leaving
/_\F(i) < 0
When free energy flows, some of it must be irreversibly dissipated,
resulting in a decrease in free energy. Not all of it is reversibly
transferred to another system or converted into another form.
In At's post, LO23569, where he is discussing the relationship between
/_\F (specifically /_\F(sy)) and W, At showed from the equation
/_\F(sy) + /_\F(su) < 0
that
/_\F(sy) < W
or
/_\F(sy) < W(sy)
which, similarly, we can show here must be true starting with the equation
/_\F(sy) = /_\F(i) + /_\F(e)
Substituting W for /_\F(e), having shown their equivalence above and
noting that /_\F(i) must always and only be negative
/_\F(sy) = /_\F(i) + W
solving for W
W = /_\F(sy) - /_\F(i)
therefore, since /_\F(i) must be negative,
/_\F(sy) < W
One of the conclusions (that I have already snipped above) that At stated
was that,
snip
>When W has a positive value, it means that some energy enters the system
>SY through work DONE ON the system. Hence F(sy) increases so that
>/_\F(sy) is positive. But when W has a negative value, it means that
>energy leaves the system through work DONE BY the system on the
>surroundings. Hence F(sy) decreases so that /_\F(sy) is negative. In other
>words, what goes in raises with a positive difference whereas what goes
>out lowers with a negative difference. This is the bookkeeping which I
>have mentioned.
end snip
This began a section where he examined first spontaneous changes by
examining different values of /_\F and W. For spontaneous changes (free
energy of the system is decreasing), he set /_\F = -5J and then examined a
range of values for W (-7J, -5J, -2J, 0J, +4J, and +8J). For
nonspontaneous changes (free energy of the system is increasing), he set
/_\F = +5J and also examined a range of values for W (-4J, 0J, +2J, +5J,
and +7J).
First, we can plug each of these values into our equation /_\F(sy) < W(sy)
and consider whether or not the situation is possible or whether it is
outside of the constraints of the laws that we have articulated and
therefore not possible. Then we can use the equation that I introduced
from Ilya Prigogine, /_\F(sy) = /_\F(i) + /_\F(e), and gain some insight
into exactly what each of these scenarios is telling us.
/_\F(sy) < W(sy)
-5J < -7J Not possible
-5J < -5J Not possible
-5J < -2J Possible, see (a) below ]
-5J < 0J Possible, see (b) below ] system is spontaneous
-5J < +4J Possible, see (c) below ] /_\F(sy) < 0
-5J < +8J Possible, see (d) below ]
+5J < -4J Not possible
+5J < 0J Not possible
+5J < +2J Not possible
+5J < +5J Not possible
+5J < +7J Possible, see (e) below ) system is nonspontaneous
/_\F(sy) > 0
Plugging our values for /_\F(sy) and (W(sy) = /_\F(e)) into /_\F(sy) =
/_\F(i) + (W(sy) = /_\F(e) = (/_\F(Ein) - /_\F(Eout)), solving for /_\F(i)
we have the following:
/_\F(i) = /_\F(sy) - (/_\F(e) or W(sy))
(a) /_\F(i) = (-5J) - (-2J) = (-3J). We can see that the magnitude of the
work done by the system on the surroundings is greater than that of the
surroundings on the system (a net outflow of free energy from the system),
and that the system has dissipated -3J of free energy in its own entropy
production internally. It is not "working" on its environment at 100%
efficiency (% efficiency = (W(sy) / /_\F(sy)) x 100 = (-2J / -5J) x 100 =
40% efficiency for the system).
(b) /_\F(i) = (-5J) - (0J) = (-5J). We can see that there is no
difference between the magnitude of work that the system is performing on
its surroundings and that which the surroundings are performing on the
system (a net exchange/flow of 0J free energy from the system), and that
the system has dissipated -5J of free energy (in its own internal entropy
production). We can know that the system is operating at 0% efficiency (%
efficiency = (W(sy) / /_\F(sy)) x 100 = (-0J / -5J) x 100 = 0%
efficiency). From this, we can know also that the system is either closed
to its surroundings (At gave the example of closed chemical reactions,
e.g., taking place in a beaker. In this case, /_\F(Ein) = 0 and
/_\F(Eout) = 0.) or is open to its surroundings with a continuous flow of
energy through the system, but is exchanging free energy with its
surroundings in such a way as to have the net exchange over the interval
of time be zero. In this case, /_\F(Ein) > 0 and /_\F(Eout) > 0, and
/_\F(Ein) = /_\F(Eout). An example of this might be a spontaneously
operating thermodynamic system with an INTERNAL difference, or entropic
force, that is converging on the organization corresponding to the state
of minimal entropy production for a given rate of energy flow through the
system - at which point it will be in a dynamic, or labile, equilibrium
state.
(c) /_\F(i) = (-5J) - (+4J) = (-9J). Here, we can see that the system is
still acting spontaneously, even though more work is being performed on
the system by its surroundings than it is performing on its surroundings.
The system is not completely transparent, so we don't know how much free
energy is flowing into or out of the system, only that the net difference
is "knowable". In this case, the system must dissipate 9J of free energy
in its own entropy production to show a net change in free energy of -5J.
Not all of the irreversible dissipation of free energy is the result of
the system's spontaneous evolution. Some portion of the free energy that
is dissipated in its entropy production is the result of the system
absorbing the entropy that is nonspontaneously imported into the system
from its surroundings.
(d) /_\F(i) = (-5J) - (+8J) = (-13J). Here again, we can see that the
system is still acting spontaneously, even though more work is being
performed on the system by its surroundings than it is performing on its
surroundings. All of what we have said about the system considered in (c)
holds true here, with the additional observation that the portion of the
dissipation of free energy in the entropy production of the system that is
due to the influx of free energy into the system is a larger percentage of
the total entropy production. As a result, we would expect that, while
the system as a whole is acting spontaneously, more of the organization
that the system exhibits will be the result of nonspontaneous exchanges
with its surroundings than in (c). As At has observed, like a large truck
hitting a car, the free energy flooding the system will most likely
decimate the organization that the system would exhibit as a result of its
own spontaneous evolution.
(e) /_\F(i) = (+5J) - (+7J) = -2J. Here we have transitioned from
spontaneous evolution to nonspontaneous evolution of the system. Overall,
the /_\F(sy) > 0. We can see that the irreversible dissipation of free
energy in the system is still negative (it always must be), but we have
the situation where the organization of the system observed is no longer
the result of its own spontaneous evolution, but rather the result of the
influence exerted on it by its surroundings.
Another aspect of the exchanges of free energy/entropy of the system with
its surroundings that cannot be considered in the present context is the
structure, or organization, of the free energy/entropy being exchanged.
When we are interested in a particular system, the organization of the
free energy flowing into the system (/_\F(Ein)) is especially critical.
Is the incoming free energy simply free energy that the system is
spontaneously importing to serve as fuel for its own entropy production?
This MAY be the case if the influx of free energy is equal to or less than
the outflow of free energy from the system (/_\F(Ein < /_\F(Eout)). Is it
in a form that aligns with the structure that the system would assume due
solely to its own, spontaneous entropy production? Is it (much more
likely) in a form that will compete with/undo the spontaneous structure of
the system? If it is the former, the system may yet reach a bifurcation
point and spontaneously emerge to an organization that is of a greater
complexity. However, any misalignment of the incoming flow of entropy
with this organization, while resulting in an increase in the rate of
entropy production, will create more of the chaos with which entropy is
typically associated than increased complexity of organization. The
overall organization of the system may actually decrease in complexity as
a result of the increased entropy production (the immergence to which At
has frequently referred) rather than increasing.
Critical in all of this is the difference between the influx of entropy
into the system (its magnitude and organization) and the SPONTANEOUS
entropy production of the system (its rate and organization). If the
spontaneous entropy production of the system is of a large enough
magnitude and a high enough level of organization, it will be able to
absorb the disruption that may result from the inundation of the system
with an influx of entropy - to a point - and maintain its own organization
(this is where At's Law of Requisite Complexity comes from). However, at
a given point, the inundation of complexity will overwhelm the system's
ability to organize itself and it will succumb to the external pressures,
its own organization collapsing/immerging.
Changes to the boundary conditions of the system that influence the
organization and rate of the OUTFLOW of energy don't affect the extent to
which the system is acting spontaneously (although it does influence the
rate of entropy production and the organization of the system). Doing
this will create a pull on the system, with its attracting, concentrating
effects. Additionally, when we increase the rate at which energy is
flowing through the system, and subsequently the rate of entropy
production within the system, by changing the rate at which energy is
flowing out of the system, we have done nothing to change the magnitude of
the entropic force acting on the system. We end up with an increase in
entropy production with no change in force and have the nonlinear
acceleration of the rate of entropy production that is necessary for a
bifurcation followed by the emergence of the system into a organization of
greater complexity.
However, increasing the inflow of free energy into the system always
adversely affects the spontaneity of the system. The rate at which
entropy is produced within the system can only be affected linearly by the
increase in the inflow of energy. As the entropic force is increased, so
the rate of entropy production will also increase. This does not
facilitate, in and of itself, reaching the phase transition that comes at
a bifurcation point. It may even preclude it. Any time that free energy
is flowing into the system, depending on the organization of this free
energy, it may have a pushing/dispersive effect on the organization of the
system, competing with the organization that the system would exhibit if
the only source of changes in the system were the result of its own
spontaneous evolution. As the balance begins to shift so that /_\F(Ein)
exceeds the change in the outflow of free energy (/_\F(Eout)), it is
almost certain that the work done on the system will have a
pushing/disruptive effect on the organization of the system. The increase
in entropy production, in such cases, will not result in the emergence of
an organization of greater complexity.
The difference between UNDOING a rheostatic, labile equilibrium and
BREAKING a homeostatic, labile equilibrium as At describes them, with
their differing qualitative outcomes (greater probability of a positive
outcome versus lesser probability of a positive outcome) is, I believe,
directly related to the effects of changing/increasing the outflow of free
energy from a system (which will have the attracting effect of the pull on
the entropy production of the system) and the changing/increasing of the
influx of free energy into a system (which will have a pushing/dispersive
effect, resulting in the destruction of the organization of the system).
This would be in harmony with the understanding of rheostasis and
homeostasis that Leo Minnigh (Greetings Leo!!!
I think that we have been thinking very much along the same lines - its
the push and the pull once again.) has articulated in his recent post of
the same name (LO25522).
Right???
Jon Krispin
--"Jon Krispin" <jkrispin@prestolitewire.com>
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