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<p>EricS -</p>
<p>Excellent (albeit dense and elaborate)... It is good to have
someone whose credentials are as high (on the topic at hand)
acknowledge your own difficult ramp up as well as some self-aware
analysis of just what made/makes it so damn hard. I hope this
helps Nick (and others) appreciate that he is not alone in his
struggles to get "traction" in this viscous soup of complex and
abstract concepts.<br>
</p>
<p>I learned my T&S in an independent study with a crusty
professor who I thought didn't like me. He apparently didn't
*not* like me but rather "wanted more for me" and decided that he
could help me through my muzzy methodologies and unleash my
(apparently) good intuition with some mano-a-mano. It worked
well (though, I still have my muzzy methodologies). We met once a
week for an hour to discuss my readings. It was the best and most
effective "class" I'd ever had (in math/science). For his part,
he was patient and positive (something he rarely showed in
lecture) and for mine, I was disciplined in my reading and in the
formulation of my questions to him when we met. As I remember it,
he credited me (us) in making it much further through the text
than would have been required for credit. I needed the same in
the Group Theory I was trying to acquire at the time but alas I
was left to trying to get it from books without guidance.<br>
</p>
<p>I suspect it was my dual major in Math which allowed me to be as
ready as I was and perhaps why he offered me the opportunity.
While we were a university there was not a graduate program in
Physics (but one in Math and one in Chemistry adjacent) and I
think many of the Physics professors were frustrated to not be
able to work with grad students in their subject... I had to take
the only Quantum Physics class from a Chemistry professor,
teaching to graduate Chemistry students with a *very* different
style and intention than I sought (and enjoyed) from my
(frustrated?) Physics professors. I got the grade in spite of not
developing much intuition in the shadow of the overbearing
mechanics of it all.<br>
</p>
<p>In closing, I will argue (without conviction but nevertheless
with confidence) that LLMs can/do do something *more* than what
you declare:</p>
<blockquote>
<p>"the language bots are handing back is the only thing it can
be; a regurgitation of the canons of the textbooks". </p>
</blockquote>
<p>My experience (and hypothesis) is that the "more" they hand back
is in the well-selected combinatorial interpolation (and some
extrapolation) they can do? </p>
<p>I think *this* is what we humans do collectively as well, we
each study and read hundreds of other precursor thinkers/writers
and then maybe spend years trying to regurgitate that to students
in a digestible form, and along the way, we develop our intuition
about which of the interpolations/extrapolations/combinatorics
that come up in that work might be useful/interesting/valid?</p>
<p>maybe.</p>
<p>- Steve<br>
</p>
<blockquote type="cite"
cite="mid:66BD46A6-2EFA-424F-9845-8A9AC1CE0CC0@santafe.edu">Yeah;
<div><br>
</div>
<div>I remember the first thermodynamics class I had. I hated it.
It all seemed like total voodoo (apologies, Dave, I don’t mean
the good kind; this is a colloquialism), and I was convinced I
would never even be able to get through it; totally give up
understanding it.</div>
<div><br>
</div>
<div>Then there was a statistical mechanics class that helped
somewhat, and with a lot of slogging (like a form of hazing), I
could get through calculations and sometimes get the right
answer. Still, there didn’t seem to be much I would have called
(then) or would call (now) “understanding”. </div>
<div><br>
</div>
<div>At some point, by very roundabout concerns, involving stuff
that overbuilds the math very heavily compared to what one needs
in equilibrium thermo, and getting even more lost in that
overhead, I finally got to the point of realizing that the main
ideas were never actually a problem. Then I got really mad at
the way this subject is taught. It never needed to be hard, not
for stupid undergrad me, nor for still-stupid but determined and
head-bashing graduate me, or for the (still not any smarter, but
I had time at SFI) ten years of going in circles with things I
could have understood much earlier with a bit more careful
presentation.</div>
<div><br>
</div>
<div>And the stuff the language bots are handing back is the only
thing it can be; a regurgitation of the canons of the textbooks.
So absolutely, it sounds no better than listening to mystics,
who mainly seem to want to tell you they have the greatest thing
in the world but they aren’t going to tell you what it is (and
_you’ll_ never understand; thats for sure!). </div>
<div><br>
</div>
<div>My own belief is that the way around this is not to retrace
the first empirical way we hit these surprises, but rather to
inherit the 100 years of related thought that has gone on since
then, and take advantage of the much simpler routes (because
they are conceptually orderly) made available at various points
in that other work. We have to have the anchoring in empirics,
of course. But that anchoring is not what ties down the concept
structure that makes the subject sensible. The difference
between good and bad presentation of the empirics is that at
least the good kind has a comprehensible unpacking.</div>
<div><br>
</div>
<div>Of course, I am not a pedagog. And what I want from it (not
getting lost) is very different from what most educators are
serving (getting very, very fast at turning the crank so you can
do your engineering job, which now is also most of what gets
done in physics.) So the things I like would probably be
completely ineffective for what the customers of the business of
education really want. Happily, I am not in charge of anything,
so the world can continue as it was.</div>
<div><br>
</div>
<div>But a lot of it comes down to forcing people to slow down and
_say what they are doing_: the kind of thing everybody finds
tedious and nobody has any patience for.</div>
<div><br>
</div>
<div>0. Is this experiencing nature, or is it setting out terms
and rules in formalism? (formalism) Deciding when the
formalism has a good binding to nature is like it generally is
in science.</div>
<div>1. What kind of systems are you modeling? Those in which the
way you set up the system fixes all of its degrees of freedom
(remember, in our formalism!), or one in which some of the
degrees of freedom are not fixed? The former is Newtonian
clockworks, the latter is thermo.</div>
<div>2. What kinds of question will you be asking? THIS ONE IS
THE KEY THAT EVERYBODY INADEQUATELY EMPHASIZES: I will be asking
question that must be answered from _distributions_. Why is
that so? Why are the phenomena you are studying such that when
you formalize them, the questions you will ask are all answered
from distributions? (and we can say, etc.) The key point that,
when an equilibrium thermo person says “state”, that is a tag
referring to some kind of distribution, focuses the attention
where it needs to be, on how many kinds of distributions there
are, and what determines them. </div>
<div>3. How do the kinds of distributions that will answer your
questions relate to the way you set up the system? Answering
this with some care gets at the difference between steady and
unsteady distributions, those that require many
boundary-condition variables to prepare and those that require
fewer, and so forth.</div>
<div>4. What is an entropy functional anyway? as a function on
distributions that just represents them by some number? What
properties do you want an entropy function to have, and how does
that tie the form you need to the characteristics of the
distribution that will answer the questions you want? This gets
at Nick’s question whether there is one entropy concept or many,
which is different from whether there is one entropy functional
form or many. Here it really is better to use what the
information-theory people have found clean good ways to say, and
to avoid intimidation, one need not even use fancy technical
words. It’s just about how one stipulates particularity out of
a field of variation, and how to attach measures to how
particular something is among its alternatives. </div>
<div>5. Finally we can get to questions about whether the
distributions that answer our questions are steady or dynamical,
whether (even if they are steady) the samples from them that
answer our questions (mathematically, called correlation
functions) would look the same if played backward in time, or
would change in some way, and so forth. That gets at what one
means by, among the vastness of possible distributions, the ones
that the tag “state” in the equilibrium-thermo jargon point at.
This is what I mean by pinning the bastards down and saying
“When you use this term “state”, you all seem to mean the same
thing by it, but I have no idea what the HELL any of you mean,
because you haven’t told me. So [please] tell me.” THIS POINT
IS AGAIN ONE OF THE CRUCIAL ONES: it gets around the oddness
that there can be entropy functions of most any distribution,
but almost-none of those are
the-entropy-that-is-a-state-function, which Frank forwarded to
Nick, or which I have referred to. And the reason they aren’t,
is that the distributions on which they are computed aren’t
those special “states” of equilibrium thermo. </div>
<div>6. There is a little clean-up that one should do, which is to
point out that getting to distributions that really are steady
and mirror-symmetric if we reverse the direction of play in time
will often whittle us down to a small number of
boundary-condition properties that we can arrange, and these
then account for the origin of pressure and temperature (or what
you like). </div>
<div><br>
</div>
<div>There’s more, but it proceeds more or less like this; very
plumber-like, or like tax forms: what line goes to what next
line? All that goes on to unpack in choices about how to use
the equations, and get us away from the goddamned focus on
energy, from which none of this makes particular sense, to a
focus on probability, where suddenly it all becomes pretty
straightforward. But most people don’t feel like listening to
this, so I won’t do it here. </div>
<div><br>
</div>
<div>So that’s the pre-processing that would fall before the
here-memorize-this “starting point” that the chatbots are mostly
handing Nick (or any of us). Rather than do that work properly
(which, you see, is not so very hard; 6 bullet points), they
will tell yarns until the cows come home, which ultimately never
contain the thing one actually needs to know, which is what
choices went into making some claim. The yarns are fine, for
getting visual and other metaphors, but they aren’t a
substitute.</div>
<div><br>
</div>
<div>Anyway. Only my opinions. Probably most people will find
the above approach appalling. But I have had a surprising
number of younger people tell me that, for the first time, they
didn’t feel lost and intimidated by it, but realized they could
navigate comfortably from these starting points. Often these
are people I didn’t meet before they told me that, but some of
them I have had longer teaching relations with. So at least for
somebody it is helpful.</div>
<div><br>
</div>
<div>Eric</div>
<div><br>
</div>
<div><br>
</div>
<div>
<div><br>
<blockquote type="cite">
<div>On Jun 18, 2025, at 12:38, steve smith
<a class="moz-txt-link-rfc2396E" href="mailto:sasmyth@swcp.com"><sasmyth@swcp.com></a> wrote:</div>
<br class="Apple-interchange-newline">
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<div>
<p>my guess is that Nick (like many of us) is just
trying to get a handle on some Thermodynamic concepts
intuitively, by making up his own simple examples and
building on them? A little
world-building/exploration by some measure?<br>
</p>
<p>Entropy is perhaps the most arcane (but not occult)
of thermodynamic concepts and in the top handful in
all of physics? Pressure, Temperature, and Volume
are roughly directly apprehensible with the likes of
Energy, Work, Ergodicity, Equilibrium, Reversibility
taking a little more thought, and Entropy, Enthalpy,
and the wycked mother of them all the Partition
Function (Z) really difficult to think about in their
own terms.</p>
<p>Entropy blends <span data-start="179" data-end="210">macroscopic
state functions</span> with <span data-start="216"
data-end="253">microscopic statistical behaviors</span>.
It resists <span data-start="268" data-end="298">single-intuition
anchoring</span>: it's about disorder, information,
irreversibility, energy quality, and more.</p>
<p>Over decades, starting with a BS in Physics, I have
been through the combinatorics of iso
baric/choric/thermal (PVT)systems and all of their
combinations, designed to implement the suite of
common cycles (rankine, stirling, otto, diesel, etc)
at different times and while that helped to carve out
an intuition for the other more abstract quantities
(like Entropy). I don't know I've ever been lead
directly to those, instead having to absorb (much of?)
the full suite of examples to begin to appreciate the
arcane (albeit not quite occult) quantities?</p>
<p>Ruth and Bruce would have a few canned examples to
work through which is sometimes a good way to get
there, but sometimes there is nothing more satisfying
than making up your own narratives and exploring their
implications, providing your world-building is
consistent and coherent. George is a very patient
copilot in such adventures, if not always the perfect
navigator?</p>
<p>I'm probably just stirring (increasing the entropy of
this thread)?<br>
</p>
<p><br>
</p>
<br>
<p><br>
</p>
<div class="moz-cite-prefix">On 6/17/25 2:47 PM, Frank
Wimberly wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAA5dAfov6aHvfmyE7mT3FrUt_QqbbnePyKD5REzEXjrRhJ0ybQ@mail.gmail.com">
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<p dir="ltr">I supplied another prompt to Géminis
which i thought would yield an illuminating
response:</p>
<p dir="ltr">What is isentropic expansion?</p>
<p dir="ltr">Isentropic expansion is a thermodynamic
process where a substance (usually a gas) expands
without any change in its entropy. This is an
idealized process, meaning it assumes two key
conditions:<br>
* Adiabatic: No heat is transferred into or out of
the system.<br>
* Reversible: There are no irreversible losses due
to factors like friction, turbulence, or
unrestrained expansion.<br>
Because entropy is a measure of disorder or
randomness in a system, a constant entropy implies
that the process is as efficient as possible, with
no energy "lost" or converted into less useful
forms.<br>
Key characteristics of isentropic expansion:<br>
* Constant entropy (\Delta S = 0): This is the
defining characteristic.<br>
* No heat transfer (\text{Q} = 0): Since the process
is adiabatic.<br>
* Decrease in temperature: As the substance expands
and does work, its internal energy decreases,
leading to a drop in temperature. This is in
contrast to an isothermal expansion where heat would
be added to maintain constant temperature.<br>
* Decrease in pressure: As the volume increases and
temperature drops, the pressure of the substance
also decreases.<br>
Why is it important?<br>
Isentropic expansion is a crucial concept in
thermodynamics and engineering for several reasons:<br>
* Idealized model: It serves as a theoretical
benchmark against which real-world processes can be
compared. No real process is perfectly isentropic,
but understanding this ideal helps engineers
evaluate how efficiently actual systems operate.<br>
* Efficiency calculations: The concept of isentropic
efficiency is used to measure how closely an actual
expansion process (like in a turbine) approaches the
ideal isentropic case. This helps in designing more
efficient engines and power systems.<br>
* Design and analysis: It's fundamental to the
design and analysis of various engineering systems,
including:<br>
* Turbines: In gas and steam turbines, hot,
high-pressure fluids expand to produce work.
Isentropic expansion helps determine the maximum
work output.<br>
* Nozzles: In applications like rocket propulsion
and jet engines, nozzles are designed to accelerate
fluids to high velocities through isentropic
expansion.<br>
* Internal combustion engines: The expansion
(power) stroke in these engines is often
approximated as an isentropic process for analysis.<br>
* Refrigeration cycles: Isentropic expansion
plays a role in these cycles as well.<br>
In essence, isentropic expansion represents the most
efficient possible expansion of a fluid, and while
it's an idealization, it provides a powerful tool
for understanding, analyzing, and optimizing energy
conversion systems.<br>
</p>
<div data-smartmail="gmail_signature">---<br>
Frank C. Wimberly<br>
140 Calle Ojo Feliz, <br>
Santa Fe, NM 87505<br>
<br>
505 670-9918<br>
Santa Fe, NM</div>
<br>
<div class="gmail_quote gmail_quote_container">
<div dir="ltr" class="gmail_attr">On Tue, Jun 17,
2025, 2:44 PM Santafe <<a
href="mailto:desmith@santafe.edu"
moz-do-not-send="true"
class="moz-txt-link-freetext">desmith@santafe.edu</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="line-break:after-white-space">Hi
Nick,
<div><br>
</div>
<div>Yes; I can report how things appear to me.
Feel free to growl that they are not correct.
I will stay away from making claims about what
things, or you, “are”. I have no access to
that.</div>
<div><br>
</div>
<div>What I see is you sort-of-demanding that
the terms that happen to interest you will be
the terms in which natural phenomena admit an
understanding. So you give more and more
elaborate descriptions of experiments and ask
about outcomes, but you leave out 2/3 of the
specification that an actual outcome would
depend on, as somebody pointed out in this
latest case about the tapping. This is why
Marcus’s advocacy of putting things into an
algorithm is so central. If a machine
generates an algorithm, it might do so by
simply making guesses about all the things you
didn’t actually tell it, but at least, for the
algorithm to exist, we will have an explicit
record of what its assumptions were. </div>
<div><br>
</div>
<div>Your comments about category errors upped
the ante on that; I see them as a premise that
the terms you choose going in, and the rules
of argument you learned in parochial school,
will grant you access through thinking to how
nature really is. That’s why I called you a
metaphysician before (and at which you
growled).</div>
<div><br>
</div>
<div>What I saw was people repeatedly telling
you that, when the part of humanity that works
in this area uses “the entropy” referring to
equilibrium, they have the property of “being
constructed to mean a state function” entailed
in that term, and then you continued to make
assertion-statements that entropy is not a
function determinable by whatever one means by
“a state”. One response to such a situation
might be to ask “Hmm; I wonder what-all they
mean when they say `a state’; they might not
be telling me enough for me to follow them.”
Or, one could conclude that they are making
category errors, and that your rules of
argument from parochial school tell you what
those errors are. Choosing to do the latter,
to me, is as close as one can get in real
life, to the pupil for whom the master pours
tea, and continues to pour after the cup is
full. The student asks why do you keep
pouring when the cup is full? etc. The
standard story.</div>
<div><br>
</div>
<div>It’s interesting: I would be the last one
to criticize anybody for trying to understand
something in other terms that occur to him,
than those that a field conventionally uses.
I very much like that mode of working, and it
is mostly what I do — not through any
greatness of soul; just because I can’t follow
other people, so I grab on where I can from my
own proclivities. Mostly I end up in a mess
that way, too. So the difference is all in
what you do when you hit a snag, and the
people around you seem to be able to
coordinate with each other enough to be
getting something done. It’s evidence, to at
least be reflected upon. </div>
<div><br>
</div>
<div>Your statement "I’ve gone back to feeling
that I don’t even know enough to ask a
question.” struck me as a glimmering of the
recognition that we don’t get to dictate to
nature the terms in which phenomena become
understandable. Those terms are something we
have to figure out along the way, along with
the rules of argument that apply to them.
Glen has written in many posts (a burst of
them a year or two ago) about the role of
embedded practice in this “coming to terms”.
Of course, we can always dictate. (We used to
say “It’s a free country”; though that seems
more awkward now.) But wherever that
dictation gets you, it won’t be understanding.</div>
<div><br>
</div>
<div>Anyway. DaveW can tell you that I don’t
understand anything about Zen or about any
contemplative tradition. (And if he can’t
tell you that, I can find others who will. It
is a *secret* in the closed hand!) But I hear
these things that come out of the various
literatures, and they often seem to me like
delightful distillations of how people are;
just the kind of things you would expect
cultures to keep and to transmit over
millennia, through innumerable hands, because
they bring the world into better focus.</div>
<div><br>
</div>
<div>Eric</div>
<div><br>
</div>
<div><br>
</div>
<div>
<div><br>
<blockquote type="cite">
<div>On Jun 18, 2025, at 1:01, Nicholas
Thompson <<a
href="mailto:thompnickson2@gmail.com"
target="_blank" rel="noreferrer"
moz-do-not-send="true"
class="moz-txt-link-freetext">thompnickson2@gmail.com</a>>
wrote:</div>
<br>
<div>
<div
style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt"> I
did not understand, and wanted to
understand, your zen comment. <span> </span><span
style="font-size:16px">I am
reluctant to ask you to punch the
tar baby again . You are, of
course, under no obligation to cure
my madness or buffer my aging. But
given the coincidence between that
comment and DaveW's, who often
presses Zen on me, I thought you
might be pointing at something there
I should pay close attention to.</span></div>
<div
style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</div>
<div
style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt">It
will be ok. You was born and bred in
a briar patch. </div>
<div
style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</div>
<div
style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt">Nick </div>
<hr
style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;display:inline-block;width:698.734375px"><span
style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline!important"></span>
<div
id="m_7979061136628741176divRplyFwdMsg" dir="ltr"
style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none"><font
style="font-size:11pt"
face="Calibri, sans-serif"><b>From:</b><span> </span>Friam
<<a
href="mailto:friam-bounces@redfish.com" target="_blank" rel="noreferrer"
moz-do-not-send="true"
class="moz-txt-link-freetext">friam-bounces@redfish.com</a>>
on behalf of Santafe <<a
href="mailto:desmith@santafe.edu"
target="_blank" rel="noreferrer"
moz-do-not-send="true"
class="moz-txt-link-freetext">desmith@santafe.edu</a>><br>
<b>Sent:</b><span> </span>Monday,
June 16, 2025 11:30 PM<br>
<b>To:</b><span> </span>The Friday
Morning Applied Complexity Coffee
Group <<a
href="mailto:friam@redfish.com"
target="_blank" rel="noreferrer"
moz-do-not-send="true"
class="moz-txt-link-freetext">friam@redfish.com</a>><br>
<b>Subject:</b><span> </span>Re:
[FRIAM] Entropy RE-redux</font>
<div> </div>
</div>
<div
style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;line-break:after-white-space">Zen
moment Nick: <br
id="m_7979061136628741176x_lineBreakAtBeginningOfMessage">
<div><br>
<blockquote type="cite">
<div>On Jun 17, 2025, at 12:00,
Nicholas Thompson <<a
href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer"
moz-do-not-send="true"
class="moz-txt-link-freetext">thompnickson2@gmail.com</a>>
wrote:</div>
<br>
<div>
<div dir="auto"> I’ve gone back
to feeling that I don’t even
know enough to ask a question.</div>
</div>
</blockquote>
<div><br>
</div>
<div>Just there for an instant, the
teacup dipped below full. btw.:
this sentence is a wonderful
encapsulation of the difference
between the metaphysician and the
scientist. Welcome back.</div>
<div><br>
</div>
<div>Frank’s language below is
good. It’s work to understand it,
of course, but the crucial
starting point is that it admits
an understanding because there is
a consistent thing being asserted.</div>
<div><br>
</div>
<div>Eric</div>
<div><br>
</div>
<blockquote type="cite">
<div>
<div dir="auto">
<div>
<div dir="ltr">
<div dir="auto">
<div>You've probably
done this. Nick.</div>
<div dir="auto"><br>
</div>
<div dir="auto">
<div dir="auto">Yes,
entropy (S) is a
state variable in
thermodynamics.</div>
<div dir="auto">Here's
what that means:</div>
<div dir="auto"> *
Definition of a
State Variable: A
state variable (or
state function) is a
property of a
thermodynamic system
that depends only on
the current state of
the system, not on
the path or process
taken to reach that
state. If a system
is in a particular
equilibrium state,
its state variables
will have specific,
unique values.</div>
<div dir="auto"> * Why
Entropy is a State
Variable:</div>
<div dir="auto"> *
Path Independence:
The change in
entropy between two
states is the same
regardless of the
reversible or
irreversible path
taken to go from the
initial state to the
final state.</div>
<div dir="auto"> *
Unique Value for a
Given State: For any
given equilibrium
state of a system
(defined by other
state variables like
temperature,
pressure, and
volume), there is a
unique value of
entropy.</div>
<div dir="auto"> *
Mathematical
Property:
Mathematically, a
quantity is a state
variable if its
differential is an
exact differential,
meaning that its
integral over a
closed path is zero.
This is true for
entropy.</div>
<div dir="auto"> *
Contrast with Path
Variables: In
contrast, quantities
like heat (Q) and
work (W) are not
state variables. The
amount of heat
transferred or work
done depends
entirely on the
specific path
followed during a
process.</div>
<div dir="auto">In
summary, entropy is
a fundamental
property that
characterizes the
state of a
thermodynamic system
and is independent
of its history.</div>
<div dir="auto"><br>
</div>
</div>
<div><br>
</div>
<div
data-smartmail="gmail_signature">---<br>
Frank C. Wimberly<br>
<a
href="https://www.google.com/maps/search/140+Calle+Ojo+Feliz,+Santa+Fe,+NM+87505?entry=gmail&source=g"
moz-do-not-send="true">140 Calle Ojo Feliz,</a><span> </span><br>
<a
href="https://www.google.com/maps/search/140+Calle+Ojo+Feliz,+Santa+Fe,+NM+87505?entry=gmail&source=g"
moz-do-not-send="true">Santa Fe, NM 87505</a><br>
<br>
505 670-9918<br>
Santa Fe, NM</div>
</div>
<br>
<div>
<div dir="ltr">On Sun,
Jun 15, 2025, 9:27 AM
Nicholas Thompson <<a
href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer"
moz-do-not-send="true" class="moz-txt-link-freetext">thompnickson2@gmail.com</a>>
wrote:<br>
</div>
<blockquote
style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div dir="ltr">
<div>Same setup as
before. Cylinder
with two
plungers and a
peggable slider
at dead center.
Lets fill our
compartments
with bbs of the
same volume.
Unpeg the
divider. Now
lets tap on the
two opposite
plungers with a
series of blows
of the same
average
magnitude but
different but
different
positive skew in
the distribution
of magnitudes.
Will the divider
move?</div>
<span>--<span> </span></span><br>
<div dir="ltr">
<div dir="ltr">
<div>Nicholas
S. Thompson</div>
<div>Emeritus
Professor of
Psychology and
Ethology</div>
<div>Clark
University</div>
<div><a
href="mailto:nthompson@clarku.edu" rel="noreferrer noreferrer"
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<span
style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline!important"> 1/2003
thru 6/2021 </span><a
href="http://friam.383.s1.nabble.com/"
style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"
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/ .-- .-. --- -. --. / ... --- -- . / .- .-. . /
..- ... . ..-. ..- .-..<br>
FRIAM Applied Complexity Group listserv<br>
Fridays 9a-12p Friday St. Johns Cafe /
Thursdays 9a-12p Zoom <a
href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,-VcislYcNK8Yb8O55nzuaeriRPKzY7veD1G7U-elrn-jaAXw_F9RG8Aq7HjjBH8v7vKOqp3ZgakJVCCWomnH6xfXvMGRFGHjfY_YWMxULES13epm4y69SiLvQmvy&typo=1"
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to (un)subscribe <a
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FRIAM-COMIC <a
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archives: 5/2017 thru present <a
href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,SjonR9S2zk_JjKCKl6RW97vvcfM_DBmBmqilbA6KL4dPTuXyBF2XfX1jtBOBtQOlCtvcPUpNNn7pbLekXGTZ6kClGfKyzJH905klO_jzSCqqSQ_pYhbSNo6I1Q,,&typo=1"
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1/2003 thru 6/2021 <a
href="http://friam.383.s1.nabble.com/"
rel="noreferrer noreferrer" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">http://friam.383.s1.nabble.com/</a><br>
</blockquote>
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<pre class="moz-quote-pre" wrap="">.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..
FRIAM Applied Complexity Group listserv
Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a
class="moz-txt-link-freetext"
href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,scI3Zb9I46TVjw3QcGcuCxQlUZ89QAHgPVXy-WLsPJVoGeu_RZId802vY15aK_XKys_dFDcsETnY_mNpnnPvmbjD-dS1y-zwM5xwO8YXrpIq&typo=1"
moz-do-not-send="true">https://bit.ly/virtualfriam</a>
to (un)subscribe <a class="moz-txt-link-freetext"
href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,UKrMRpldBuRW0or6rODl9peXzhW4h7BNcndiY_pWoBJrD1jcoNlYA-sTyE8DrodhmhsrMg9AINEyr482BNo3wpmObV2l4LMCOA7l2QhvBfq1MqBLgqxB&typo=1"
moz-do-not-send="true">http://redfish.com/mailman/listinfo/friam_redfish.com</a>
FRIAM-COMIC <a class="moz-txt-link-freetext"
href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,APLBZHasUmyTXdQBbK400g3OcArYUiQHeLIYehkmXfnHGMoFHuevwtgA3wCx1vhDTD1j-4OkxpaVnslqiq0_JFc9U2h3uEN2UhSRdT2CsH2z3_1Wa3Cbn4A,&typo=1"
moz-do-not-send="true">http://friam-comic.blogspot.com/</a>
archives: 5/2017 thru present <a class="moz-txt-link-freetext"
href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,8lI_F3hDpcCPpIR-iXQAS-BPaHcGjloFODJr53zO18ZuIvuBhDhvGzTLaQVyhqDn19eRKkoCWzf8VIPNY9g92RlLBNoxE5MetgTMKO1hj0Sd3g,,&typo=1"
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1/2003 thru 6/2021 <a class="moz-txt-link-freetext"
href="http://friam.383.s1.nabble.com/"
moz-do-not-send="true">http://friam.383.s1.nabble.com/</a>
</pre>
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.-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-.
--- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..-
.-..<br>
FRIAM Applied Complexity Group listserv<br>
Fridays 9a-12p Friday St. Johns Cafe / Thursdays
9a-12p Zoom
<a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,eOR6lXHbkz9FDp_F5EhvtBdVA011L8K9ntJGytID_gg0tuW1mbXJJIh1Ao_DveQtQClCQf5VHo_KZ-aJZqhB43Z8l02-HMRur-tQnD7uRjdvnCQhnaU,&typo=1">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,eOR6lXHbkz9FDp_F5EhvtBdVA011L8K9ntJGytID_gg0tuW1mbXJJIh1Ao_DveQtQClCQf5VHo_KZ-aJZqhB43Z8l02-HMRur-tQnD7uRjdvnCQhnaU,&typo=1</a><br>
to (un)subscribe
<a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,3R-CpTO75xCb8a586XMCGfZNO4N1YAqWott72o-esdXhNom1IZwQciEW4YoNVNtUa-GzzfnrBSQMGYflcmc70H3uUPWL9v86gfaaWBreVKH_iaI5E9r1qER0gj-C&typo=1">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,3R-CpTO75xCb8a586XMCGfZNO4N1YAqWott72o-esdXhNom1IZwQciEW4YoNVNtUa-GzzfnrBSQMGYflcmc70H3uUPWL9v86gfaaWBreVKH_iaI5E9r1qER0gj-C&typo=1</a><br>
FRIAM-COMIC
<a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,iP5UtG9cXGZb9iFbdK7S9-wjB-lxbUCrHrAJVtf8z4uHkrqHO2zXuOiFjR7LQD9MgGajU2fDwW1MHM4C9zspD9Xd6RL9W6GGCEBVt4icMjO1fW4FEsk,&typo=1">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,iP5UtG9cXGZb9iFbdK7S9-wjB-lxbUCrHrAJVtf8z4uHkrqHO2zXuOiFjR7LQD9MgGajU2fDwW1MHM4C9zspD9Xd6RL9W6GGCEBVt4icMjO1fW4FEsk,&typo=1</a><br>
archives: 5/2017 thru present
<a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,2-ZbJ6GSm8x03lzF6kWDloQOmS-ED-aQOkQE2Jqjsxdm33er5ijqoQTRCTHLzTqrrCEa1WfYUnK49Bs6T8bg40GTs-qw08LIBLBeh6480UGC6GSfvlxXbfnc8g,,&typo=1">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,2-ZbJ6GSm8x03lzF6kWDloQOmS-ED-aQOkQE2Jqjsxdm33er5ijqoQTRCTHLzTqrrCEa1WfYUnK49Bs6T8bg40GTs-qw08LIBLBeh6480UGC6GSfvlxXbfnc8g,,&typo=1</a><br>
1/2003 thru 6/2021 <a class="moz-txt-link-freetext" href="http://friam.383.s1.nabble.com/">http://friam.383.s1.nabble.com/</a><br>
</div>
</blockquote>
</div>
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</div>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..
FRIAM Applied Complexity Group listserv
Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a class="moz-txt-link-freetext" href="https://bit.ly/virtualfriam">https://bit.ly/virtualfriam</a>
to (un)subscribe <a class="moz-txt-link-freetext" href="http://redfish.com/mailman/listinfo/friam_redfish.com">http://redfish.com/mailman/listinfo/friam_redfish.com</a>
FRIAM-COMIC <a class="moz-txt-link-freetext" href="http://friam-comic.blogspot.com/">http://friam-comic.blogspot.com/</a>
archives: 5/2017 thru present <a class="moz-txt-link-freetext" href="https://redfish.com/pipermail/friam_redfish.com/">https://redfish.com/pipermail/friam_redfish.com/</a>
1/2003 thru 6/2021 <a class="moz-txt-link-freetext" href="http://friam.383.s1.nabble.com/">http://friam.383.s1.nabble.com/</a>
</pre>
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