<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">What Stephen has here is okay, in that it is also the tribal chant of a certain tribe, who can use it to do correct calculations as long as they remain within a bunch of further assumptions that are not articulated well.<div><br></div><div>But the sequence below is actually a mess. Not because it needs to be. But because, for convenience of calculation, people narrow the cases they will consider quite severely, in a way that makes the quantities they compute much less entirely the outcomes of principles, and more of a mixture of principles and ad hoc assumptions and restrictions of the cases treated. Figuring out what _those_ guys are doing remains enough of a mess that most people today don’t seem to be clear on it, whereas the case of equilibrium strips away the need for enough ad-hoccery that you can state the principles and then show how they lead to particular constructions.</div><div><br></div><div>I have been tearing hair for years, trying to figure out why these guys speak as if they have a general construction, and well-defined terms, when it is manifest that they have a bunch of special cases and choices. The past summer, I had a week in Corsica hosted by some people who work in this area, whom I really like. Unlike a godforsaken paper, you can ask a question of a person. And on an island where people can’t get away, as long as they don’t throw you into the sea you can keep asking until (in the case that your interlocutor is a person of good faith and some sense) you get an answer to the question you actually asked. So I kept pushing on “why do you make this substitution which is not general and which throws away information that impacts the dynamics?” And finally I got back “Yes, we know it does all those things, and we recognize what information it throws away. But if we didn’t make all these restrictions, how would we do calculations in a manageable way?” So no more hair tearing on my end. They understand, and probably have always understood, the ad hoccery. They just never mention it because it is something they all do in the same way, and they are willing to live with it because by limiting their aspirations, then can at least get some pieces of work done. (And a lot is, properly, nicely handled within those ad hoc assumptions, which is why this is a “thriving” community.)</div><div><br></div><div>Just written here as a note of caution. If you want to understand what role principles are playing, and don’t yet, deal with the equilibrium case until you can get through the fog of bad and incomplete representations of it. There will be plenty more work to do, to deal with the case Stephen has below, to recognize which parts are the same principles, and what-all they are buried in.</div><div><br></div><div>Eric</div><div><br></div><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Jun 18, 2025, at 1:50, Stephen Guerin <stephen.guerin@simtable.com> wrote:</div><br class="Apple-interchange-newline"><div><div dir="auto"><div dir="auto">And a follow up on Frank's prompt which was for equilibrium where the integral /change of entropt was zero to out of equilibrium systems like weather.</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">
Entropy (S) in Thermodynamics and Beyond</div><div dir="auto"><br></div><div dir="auto">Definition of a State Variable (Equilibrium Context):</div><div dir="auto">A state variable depends only on the system’s current equilibrium state, not on the path taken to reach it.</div><div dir="auto">In equilibrium, entropy is one such state variable: its value is uniquely determined by macroscopic variables like T, P, V.</div><div dir="auto"><br></div><div dir="auto">Entropy in Nonequilibrium Systems</div><div dir="auto">Local Entropy:</div><div dir="auto"> Out of equilibrium, we can often define a local entropy density s(r,t) based on local variables (if local equilibrium holds).</div><div dir="auto"> S_total = ∫ s(r,t) dV</div><div dir="auto"> but this depends on internal gradients, flows, and structure — no single global state function S(T,P,V) describes the system.</div><div dir="auto"><br></div><div dir="auto">Entropy Production:</div><div dir="auto"> In nonequilibrium systems, the total entropy changes due to both exchange and internal production:</div><div dir="auto"> dS = δQ/T + dS_gen</div><div dir="auto"> where dS_gen > 0 for irreversible processes (e.g., viscous dissipation, heat conduction).</div><div dir="auto"><br></div><div dir="auto">Negentropy and Free Energy:</div><div dir="auto"> Systems far from equilibrium possess negentropy — a measure of their potential to do work or sustain structure.</div><div dir="auto"> Free energy reflects this potential:</div><div dir="auto"> F = U - T S</div><div dir="auto"> More negentropy → more free energy → greater capacity for work or structure formation.</div><div dir="auto"><br></div><div dir="auto">Closed Path Integrals:</div><div dir="auto"> In equilibrium: ∮ dS = 0 (S is exact differential)</div><div dir="auto"> Out of equilibrium: ∮ dS = ∮ dS_gen > 0 (irreversibility generates entropy)</div><div dir="auto"><br></div><div dir="auto">Summary:</div><div dir="auto"> In equilibrium, entropy is a state variable with a unique value for each state.</div><div dir="auto"> Out of equilibrium, entropy production, local entropies, and negentropy describe the system’s internal structure and potential to do work.</div><div dir="auto"> The simple equilibrium picture no longer applies.<br><hr><p><br></p></div><div data-smartmail="gmail_signature" dir="auto">____________________________________________<br>CEO Founder, <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fSimtable.com&c=E,1,RyijCbsd-IZng14nOpQ-Tfrz7oS06rrLWJpwWg-yy1jaWqEa3zXDmG-szq2h-nejtW4rNI6RLNavgsuFmR9KpK6HCtlVSAEOIW8VlsnaC0GnNU2J4noZNj8vZA,,&typo=1&ancr_add=1">Simtable.com</a><br><a href="mailto:stephen.guerin@simtable.com" rel="noreferrer noreferrer" target="_blank">stephen.guerin@simtable.com</a> <br><br>Harvard Visualization Research and Teaching Lab<br><a href="mailto:stephenguerin@fas.harvard.edu" rel="noreferrer noreferrer" target="_blank">stephenguerin@fas.harvard.edu</a><br><br>mobile: (505)577-5828</div><br><div class="gmail_quote" dir="auto"><div dir="ltr" class="gmail_attr">On Mon, Jun 16, 2025, 2:02 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" rel="noreferrer noreferrer" target="_blank">wimberly3@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><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" rel="noreferrer noreferrer" target="_blank">140 Calle Ojo Feliz, </a><br><a href="https://www.google.com/maps/search/140+Calle+Ojo+Feliz,++Santa+Fe,+NM+87505?entry=gmail&source=g" rel="noreferrer noreferrer" target="_blank">Santa Fe, NM 87505</a><br><br>505 670-9918<br>Santa Fe, NM</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jun 15, 2025, 9:27 AM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" rel="noreferrer noreferrer noreferrer" target="_blank">thompnickson2@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid 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 class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature"><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 noreferrer noreferrer" target="_blank">nthompson@clarku.edu</a></div><a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson&c=E,1,dFySm0aH5eG1p6xR6886mol3FkaFAFtbDQ-wOyAcOvL0ibZtWbjM2EFJyRjtgW59o8bjlLjQIH_zCV4OKkS22BbKyIifWbo2_Fu35RFtlL6a40lRe28GCxD-Ug,,&typo=1" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://wordpress.clarku.edu/nthompson</a></div></div></div></div>
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