[continued]
>DB>In the special case of certain far-from-equilibrium systems
>>Prigogine has shown that the SLOT can, under certain
>>circumstances, drive the spontaneous formation of macroscopic
>>dissipative structures that *function as* energy- conversion
>>systems. For instance, the disequilibrium maintained in the earth's
>>ocean-atmosphere system allows the formation of hurricanes (or
>>typhoons or cyclones depending on where they form). Such a storm
>>can be thought of as a kind of heat engine doing macroscopic work
>>on its environment as energy is taken from the warm ocean surface
>>and dissipated as waste heat in the upper atmosphere, which then
>>cools by radiation into outer space and by advection into colder
>>climes via the motion of the tropical Hadley cells.
>
SJ>This is interesting but I fail to see the relevance of Prigogine's
>"far-from-equilibrium systems" to living systems. Thaxton et al
>consider Prigogine's claims:
> <SNIP TB&O quote>
My example of Prigogine's dissipative structures in general, and of
tropical storms in particular, above was not given for their application
to living systems; they were given as a counterexample to the idea that
some sort of external energy conversion system is required for a system
to
spontaneously organize and display complex structure and behavior in
order
to avoid being forbidden by the SLOT. The example is a macroscopically
complex one with complex behavior that spontaneously forms without the
help of some prior 'energy conversion system'. The degree of macroscopic
complexity in organization and behavior of a hurricane/typhoon is greater
than that of an equivalent mass of a calm atmosphere (under similar
temperature, humidity, etc. conditions). After the system forms it
becomes
its own 'energy conversion system' and acts like a spontaneously forming
heat engine doing macroscopic work while processing a throughput of
thermal
energy.
SJ>However, they point out that "such analogies have scant relevance to
>the origin-of-life question" because they fail to distinguish between
>the order of non-living systems and the specified compexity of living
>systems:
> <SNIP TB&O quote>
OK, Prigogine does not consider systems with 'specified complexity' and
TB&O claim that living systems possess it. Then they claim that this
invalidates any possible relevance of Prigoginian dissipative structure
formation to the OOL problem. It is not clear to me that such an
invalidation necessarily follows. Their conclusion is a non sequitur.
Maybe dissipative structures are not helpful in understanding the OOL,
but
the (quoted) argument given by TB&O doesn't show this. Do TB&O happen to
give a useful objective definition of 'specified complexity', and if so,
do they give a formula as how to calculate it, and do they introduce any
physical dynamical laws describing how 'specified complexity' behaves in
interaction with other physical properties? If so, what are the
equations
describing those dynamical laws?
SJ>A second criticism they have is that because such ordering within
>the system arises through constraints imposed at the system boundary,
>the system order and complexity, cannot exceed that of its environment:
> <SNIP TB&O quote>
Why not? Is this a new law of nature that TB&O have discovered? If it
is
some universal 'specified complexity' law, it is not the SLOT and any
invocation of the SLOT as precluding the senario is suspect and most
likely
invalid.
SJ>In particular, they point out that the special boundary conditions
>requireed by Prigogine's model would be "a miracle in its own right":
> <SNIP TB&O quote>
Maybe it would be a 'miracle' and maybe it wouldn't. In any event, what
does this have to do with the SLOT?
SJ>Thaxton et al's final points are that Prigogine's autocatalytic
chemical
>reactions have not been been demonstrated experimentally to have any
>real correspondence to prebiotic condensation reactions and they do not
>offer an explanation as to how the configurational entropy work was
>accomplished under prebiotic conditions:
> <SNIP TB&O quote>
I had only said that such behavior way *suggestive* for the OOL problem.
I
did not say that dissipative structures solved the problem (in fact, I
went out of my way to emphasize this point). TB&O do not demonstrate (in
the quotes given) that such dissipative structures are irrelevant. They
do
validly point out that any required dissipative structure system would
have
to be *much* more complicated than those examples put forth so far by the
likes of those Prigogine has championed. They review the past history or
experimental failure so far in this regard, and also seem to express
incredulity that any such structures could ever do the job. This is not
a
demonstration of impossibility or of irrelevance however.
>DB>Some spontaneous processes work without any special energy-conversion
>>mechanism, some of them grow their own energy-conversion mechanisms,
and
>>some of them operate using previously existing such mechanisms. In any
event,
>>the presence or absence of such a mechanism is not a concern of the
SLOT.
>
>How about giving examples of these "spontaneous processes" which "grow
>their own energy-conversion mechanisms".
I just gave one above of hurricanes/typhoons. I also mentioned in part A
of this post the example of the formation of stars and planetary systems
out of interstellar gas clouds. A star *is* a spontaneously forming
energy conversion system, and its structure and behaviour is more
complicated than a static cloud of gas (even though it has less entropy).
There are hosts of such examples in many areas of science. For example,
in
geology/geophysics consider plate tectonics. This is a process driven by
a
thermal disequilibrium maintained by the temperature difference between
the
earth's core and its crust. Convective cells in the mantle spontaneously
form and carry the crustal plates 'along for the ride'. Macroscopic work
is done by the lifting of chunks of crust up against the earth's
gravitational field in the formation of mountain ranges. This stored
potential energy was converted from random thermal energy inside the
earth.
In botany photosynthesis in plants is a spontaneously forming energy
conversion system that converts the thermal energy of sunlight into
stored
potential energy of high energy chemical bonds in the production of
carbohydrates. Each plant grows its energy conversion system from its
environment. A seed or a zygote does not have such an energy conversion
system. (It does have a set of instructions for building one though,
along
with a kernel system that can bootstrap the construction of such an
energy
conversion system from its environment. But the fact remains that a
zygote
of an oak tree does not possess a photosynthetic apparatus.) There are
lots of other examples from many areas of science, but I refuse to take
up
more room here by mentioning them.
>DB>Before I get into this point let me mention that a couple of the
>>quotes that Steve gave from his daughter's introductory physics
>>book by Giancoli are misleading and just about hopelessly
>>confused.
>
SJ>I agree that Giancoli's is an "introductory physics book", but I await
>your evidence that he is "hopelessly confused".
>...
I said that the quotes were just about hopelessly confused. I don't know
whether or not Giancoli is confused. Maybe he just explained himself
badly. (Maybe Steve accidently miscopied some of Giancoli's words.)
Below is a copy of the first (that I noticed in the last few posts in the
current thread) Giancoli quote that Steve gave.
>"In general, we associate disorder with randomness salt and pepper in
>layers is more orderly than a random mixture; a neat stack of
>numbered pages is more orderly than pages strewn randomly about on
>the floor.
Randomness connotes an event or process that is either uncaused or one
where, at the least, the causal conditions are inaccessible to
observation.
(In the second instance it may be argued that the process is only
*apparently* random, however.) Disorder, OTOH connotes an arrangement
of
the parts of a whole such that a pattern is not discernable and a
description of the arrangement is necessarily a long one. It is true
that
if the arrangement of the parts of a whole is freely and wholely
determined
by a random process then the result will be a disordered arrangement. It
is also possible, though, for a disordered arrangement to be the result
of
a purposeful (but complicated) nonrandom process. Thus any association
between disorder and randomness is not an identity. Giancoli is
*correct*
about the salt, pepper, and arrangements of pages above, however.
> We can also say that a more orderly arrangement is one
>that requires more information to specify or classify it.
This is hopelessly confused. Actually, it is precisely backwards. A
more
*dis*orderly arrangement is one that requires more information to specify
or classify it. A more orderly arrangement requires *less* such
information.
> When we
>have one hot and one cold body, we have two classes of molecules and
>two pieces of information; when the two bodies come to the same
>temperature, there is only one class and one piece of information.
This is confusing to the reader unless a careful definition of "piece of
information' is given. In order to be correct a "piece of information"
as described here cannot be a bit, or, any fixed multiple unit of bits.
Also Giancoli doesn't say how he proports to classify the molecules into
one or two classes. Both bodies have broad distributions of molecular
speeds and energies, so I doubt that he would classify them according to
their individual speeds--especially since the probability distribution of
speeds depends on the mass of the molecules, and if the bodies are
composed
of multiple types of molecules then each molecular type has its own speed
distribution anyway. At least if the classification is according to
translational kinetic energy then the distribution of that translational
kinetic energy depends solely on the temperature. Even then, though, the
hot body will have some low (translational kinetic) energy molecules. and
the cold body will have some high energy molecules. If both bodies have
the same temperature then they will have the same distribution of
individual molecular translational kinetic energies if the temperature
is high enough for classical (non quantum) stat mech to hold for the
system. Otherwise (as in the case of delocalized electrons in solids)
the
result is material dependent and much more complicated.
>When salt and pepper are mixed there is only one (uniform) class;
>when they are in layers, there are two classes. In this sense,
>information is connected to order, or low entropy.
Both order and low entropy are associated with *little* information, and
OTOH disorder and high entropy are associated with *much* information.
As
far as the distribution of salt and pepper grains in a salt/pepper shaker
goes, the layered distribution requires *less* information to specify
exactly where all the grains are (and is therefore more orderly), whereas
the uniformly mixed shaker case requires *more* information to specify
where each of the grains are, and is consequently more disordered.
Giancoli does not make this clear. Rather, he seems to intimate that
*more* information is associated with order and low entropy.
> This is the
>foundation upon which the modern field of information theory is
>built." (Giancoli D.C, "Physics", 1991, p403)
Fortunately, the foundation of info theory is more secure than the
description given by the above passage from Giancoli.
>"...the entropy of a system can be considered a measure of the
>disorder of the system. Then the second law of thermodynamics can be
>stated simply as: Natural processes tend to move toward a state of
>greater disorder." (Giancoli D.C, "Physics: Principles with
>Applications", 1991, p402)
This is a common way of putting things, but for this to be true we would
have to redefine the notion of disorder to map more closely to the notion
of thermodynamic entropy than is the case with the usual meaning of the
term disorder. Normally we think of disorder as a property of a given
arrangement, but the idea of entropy is that it is a statistical function
which is averaged over a distribution of possibilities, and is not
determined by a given arrangement. Even if we make the meaning of
disorder
close enough to that of entropy so that entropy can measure it, we still
need to make clear that the disorder in question is at the level if the
individual microscopic degress of freedom, and not at the level of some
macroscopically observable pattern (simple or complex) which may or may
not be present. Consequently, the natural tendency in question is
associated with the microscopic degrees of freedom--and even here--(it
only
applies in the form stated above) to isolated systems. (The SLOT does
apply to non-isolated and open systems, but in that case the phrasing of
it needs to be tightened up.)
>"From these examples, it is clear that probability is directly
>related to disorder and hence to entropy. That is, the most probable
>state is the one with greatest entropy, or greatest disorder and
>randomness.
Here it needs to be mentioned that the "state" whose probability is being
discussed is a given macroscopic state taken from a collection of other
macroscopically distinguishable states, all of which are accessible to
the system's microscopic dynamics which is less constrained by the
boundary
conditions than the resolution used to distinguish those macroscopic
states. If the reader thought that the term 'state' above was the
microscopic state, he/she would be wrong, since all accessible
microscopic
states are (for an isolated equilibrated system) equally likely (i.e.have
the same probability), and the entropy is not even defined for each of
them separately anyway.
> Boltzmann showed that, consistent with Clausius's
>definition (/\S= Q/T), the entropy of a system in a given (macro)
>state can be written: S=2.3 k log W, where k is Boltzmann's constant
>(k = 1.38 x 10^-23 J/K) and W is the number of microstates
>corresponding to the given macrostate; that is, W is proportional to
>the probability of occurrence of that state.
This is OK as long it is clearly understood that Clausius' formula above
is
for a *reversible* process only.
> In terms of
>probability, the second law of thermodynamics-which tells us that
>entropy increases in any process- reduces to the statement that those
>processes occur which are most probable.
This is not quite right. Giancoli has, incorrectly, reduced the SLOT to
the tautology that the more probable things tend to happen more
frequently.
The SLOT concerns an arrow of time. The reduced statement above does
not,
and instead refers to what happens at a given time rather than the
tendency
of of how things happen over the course of time. The run-on paragraph-
sentence below more accurately (but less understandably and less
succinctly) describes the probablistic interpretation of the SLOT (for an
isolated system).
Since the entropy measures the uncertainty in or the randomness of the
distribution of the accessible microstates, or equivalently, the
logarithm
of the effective number of the possible microstates that the system may
choose from those consistent with the observed macrostate, the SLOT in
terms of probability, becomes the statement that (for an isolated system)
the distribution of microstates becomes evermore random or more
uncertain,
and that the effective number of possible microstates allowed for the
system continues to grow with time until the state of maximal randomness
is
reached where all the microstates consistent with the macroscopic
constraints on the system become equi-probable, at which time the system
is in equilibrium and the entropy stops rising.
> .... The second law thus becomes
>a trivial statement.
The SLOT is not trivial. Gioncoli merely trivializes it.
> However, there is an additional element now.
>The second law in terms of probability does not forbid a decrease in
>entropy. Rather, it says the probability is extremely low. It is
>not impossible that salt and pepper should separate spontaneously
>into layers, or that a broken tea cup should mend itself. It is even
>possible that a lake should freeze over on a hot summer day (that is,
>for heat to flow out of the cold lake into the warmer surroundings).
>But the probability for such events occurring is extremely small."
>Giancoli D.C, "Physics", 1991, p406)
It is true that such weird events have a *very* low--yet nonzero--
probability, but it is not necessarily true that such an event would
correspond to a decrease in the system's entropy. Whether such an event
would reduce the entropy or not depends on subtle details about just how
one precisely defines the macrostate for the system at hand.
>"The ideas of entropy and disorder are made clearer with the use of a
>statistical or probabilistic analysis of the molecular state of a
>system. This statistical approach, which was first applied toward
>the end of the nineteenth century by Ludwig Boltzmann (1844-1906),
>makes a clear distinction between the "macrostate" and the
>"microstate" of a system. The microstate of a system would be
>specified when the position and velocity of every particle (or
>molecule) is given. The macrostate of a system is specified by
>giving the macroscopic properties of the system-the temperature,
>pressure, number of moles, and so on. In reality, we can know only
>the macrostate of a system. There are generally far too many
>molecules in a system to be able to know the velocity and position of
>every one at a given moment. Nonetheless, it is important to
>recognize that a great many different microstates can correspond to
>the same macrostate.
I agree with all of this (except a tiny almost insignificant detail about
the specification of the microstate which requires the particle's
momentum
rather than its velocity.)
> Let us take a simple example. Suppose you
>repeatedly shake four coins in your hand and drop them on the table.
>Specifying the number of heads and the number of tails that appear on
>a given throw is the macrostate of this system. Specifying each coin
>as being a head or a tail is the microstate of the system." Giancoli
>D.C, "Physics, 1991, pp404-405)
I agree with this too (except for another tiny detail where I would say
that the various parts of the coin analogy are *like* or analogous to the
macrostate and microstates of a thermodynamic system, rather than saying
that the corresponding parts of the coin analogy *are* the macrostate and
microstates). I would also choose much more than four coins in the
analogy to make it more similar to a thermodynamic system where the
number
of microscopic variables (degrees of freedom) associated with a given
macroscopic variable is many orders of magnitude large.
SJ>But I would appreciate you giving me reasons why I should accept your
>"authority" instead of "Giancoli's"?
I suggest that you study and learn the subject for yourself and then you
can rely on your own authority rather than on the watered down,
ambiguously
phrased, unqualified, sometimes overdrawn, sometimes misleading,
occasionally incorrect, often correct, sometimes elegant, and
occasionally
exquisite layman's level conclusions of others. My criticism's of
Giancoli's treatment of entropy and the SLOT are not to be taken as a
blanket dissing of his entire book. I'm sure that there are many
(probably
most) topics where the simplifed treatment and explanations are
essentially
harmless and are just fine for an introductory book. It's just very
difficult to get everything exactly right in a book that is supposed to
cover every area of physics. For instance, at my college we use an
introductory textbook that, in my opinion, does a poor job of explaining
the special theory of relativity by introducing (and advocating the use
of)
the concept of a velocity-dependent relativistic mass. Such a treatment
abuses the modern meaning of 'mass' as physicists understand it, and
obscures the structure of the theory. My objection to the treatment is
mostly based on the asthetics of the theory (which the students can't
appreciate at the lower level anyway). Other parts of the book are just
fine, being well written, understandable, and close enough to the truth
for
the necessary purposes of an introductory course. Even in the relativity
section the misrepresentations are ultimately minor enough so that for
nearly any student that is not going to go to graduate school and major
in
high energy particle physics will not be harmed too badly by its
treatment.
So on balance we don't mind using the book for the course. I suspect
that
similar calculated trade offs were made in the choice of textbook for
your
(Steve) daughter's introductory physics course.
Responding to Steve here has exhausted me and has consumed much more of
my
time than is prudent. I therefore do not wish to further discuss this
thread
at this time. I apologize to any reader who may actually still be left
here
reading the end of this post for its excessive length.
David Bowman
dbowman@gtc.georgetown.ky.us