<div dir="ltr">Nick,<br>You pretty much nailed it.<br>But… maybe only 99.99% nailed it 😉<br><br>You said:<br><br>"If you put a bunch of energy into a system by heating, you can NOT recover all of that energy as work."<br><br>In the real world, you're absolutely right. But in theoretical physics land — where unicorns wear lab coats — it’s actually possible to recover all of that energy.<br><br>Here’s the trick:<br>If you have a heat source at some random temperature and a perfect heat sink at absolute zero, then yes — you can get back all the energy as work.<br>But as the temperature of the heat sink goes up, your ability to recover energy goes down.<br>If the sink is nearly as hot as the source? You get next to nothing. Welcome to entropy.<br><br>Now let’s imagine a silly little thought experiment:<br><br>You’ve got Earth spinning around the sun, heating up during the day, cooling at night.<br><br>But imagine night-time cools the whole planet to absolute zero. (Yes, the kind of cold that scares even penguins.)<br><br>You also have a magic cylinder that you can open, close, and isolate perfectly.<br><br>Here's what you do:<br><br>At night, open the cylinder and let any warm air out. Let in some of that chilly absolute-zero air. Lock the piston in place.<br><br>Close the vents (but don’t insulate yet) and wait for sunrise.<br><br>As the day warms up, the air in the cylinder heats up and pressure builds.<br><br>Once it’s as hot as it’s going to get — wrap it up in a warm, fuzzy thermal blanket (okay, maybe not fuzzy) and seal it off completely.<br><br>Now wait until the next freezing midnight, when Earth is back at absolute zero.<br><br>Unlock the piston and let the expanding gas do work as it pushes outward.<br><br>Voilà! In this perfect little imaginary world, you've recovered all the heat energy as mechanical energy.<br><br>The real world never works quite this neatly — but that gap between theory and reality? That’s where entropy sneaks in and steals your lunch.</div><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">On Thu, 3 Jul 2025 at 23:42, Sarbajit Roy <<a href="mailto:sroy.mb@gmail.com">sroy.mb@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 class="gmail_default" style="font-family:verdana,sans-serif">As I am primarily a Mechanical Engineer, who learnt The Uncertainty Principle in Sem 1, and Thermodynamics 101 in Sem 2, I couldn't then, nor, now reconcile Boltzmann's <br><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;width:min-content;display:inline-block;color:rgb(44,44,54);font-family:KaTeX_Main,"Times New Roman",serif;font-size:19.36px;letter-spacing:0.32px;text-align:center"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;font-family:KaTeX_Math;font-style:italic;margin-right:0.05764em">S = k.ln</span></span><span style="color:rgb(44,44,54);font-family:KaTeX_Main,"Times New Roman",serif;font-size:1.21em;letter-spacing:0.32px">Ω <br></span><span style="color:rgb(44,44,54);font-family:KaTeX_Main,"Times New Roman",serif;font-size:15.73px;letter-spacing:0.32px">to all that statistical</span> Omega <span style="color:rgb(44,44,54);font-family:KaTeX_Main,"Times New Roman",serif;font-size:1.21em;letter-spacing:0.32px">fuzzy stuff and so stick to the classical theory which ignores micro/macrostates, and I've not had issues through my ignorance..</span></div><div class="gmail_default" style="font-family:verdana,sans-serif"><span style="color:rgb(44,44,54);font-family:KaTeX_Main,"Times New Roman",serif;font-size:1.21em;letter-spacing:0.32px"><br><br></span></div><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;width:min-content;display:inline-block;color:rgb(44,44,54);font-family:KaTeX_Main,"Times New Roman",serif;font-size:19.36px;letter-spacing:0.32px;text-align:center"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;text-align:left"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;border-collapse:collapse;display:inline-table;table-layout:fixed;margin-right:0px"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:table-row"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:table-cell;vertical-align:bottom;height:0.3283em"><br></span><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:table-cell;font-size:1px;min-width:2px;vertical-align:bottom;width:2px"></span></span><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:table-row"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:table-cell;vertical-align:bottom;height:0.15em"><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:block;height:0px"></span></span></span></span></span></span><span style="box-sizing:border-box;border-width:0px;border-style:solid;border-color:currentcolor;display:inline-block;margin-right:0.1667em"></span><br></span></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Jul 4, 2025 at 3:00 AM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" 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>Thanks Sarbajit, </div><div><br></div><div>George and I have been working on a way of understanding this asymmetry which is kinda neat. Here is George's summary of our conversation. The gist of it is that while you can bring chambers to the same temperature by heating and compressing, they are in different macrostates because aside effect of compression is an increase in density which heating does not produce. </div><div>See:</div><div><a href="https://chatgpt.com/canvas/shared/6865db6493e88191a9023926478b3c01" target="_blank">https://chatgpt.com/canvas/shared/6865db6493e88191a9023926478b3c01</a></div><div><br></div><div>Nick</div><div><br></div><div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jul 3, 2025 at 4:08 PM Sarbajit Roy <<a href="mailto:sroy.mb@gmail.com" target="_blank">sroy.mb@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 class="gmail_default" style="font-family:verdana,sans-serif">It has been a very long time (too long) since I studied the 2nd law or Shannon. It's all very veiled and foggy just now, however,
I have often wondered if Entropy is fundamentally about ignorance, correlations, or something deeper?
</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jul 3, 2025 at 11:47 PM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" 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>Dear Long Suffering Friamers</div><div><br></div><div>I think I have now managed to come up with a macrostate statement of a phenomenon that requires entropy for its understanding. It parallels Lincoln's aphorism about fooling all of the people. </div><div><br></div><div><b style="font-family:"comic sans ms",sans-serif">Assuming friction free and quasistatic motion and total insulation where appropriate:</b></div><div><span style="font-family:"comic sans ms",sans-serif"></span><br><div style="margin-left:40px"><span style="font-family:"comic sans ms",sans-serif"></span><b style="font-family:"comic sans ms",sans-serif">If you put a bunch of energy into a system by working on it,</b><b style="font-family:"comic sans ms",sans-serif">you can recover all that energy as work.</b></div><div style="margin-left:40px"><span style="font-family:"comic sans ms",sans-serif"></span><br><span style="font-family:"comic sans ms",sans-serif"></span><b style="font-family:"comic sans ms",sans-serif">If you put a bunch of energy into a system by heating it,</b><b style="font-family:"comic sans ms",sans-serif">you can recover all that energy as heating,</b></div><div style="margin-left:40px"><span style="font-family:"comic sans ms",sans-serif"></span><br><span style="font-family:"comic sans ms",sans-serif"></span><b style="font-family:"comic sans ms",sans-serif">If you put a bunch of energy into a system by working on it,</b><b style="font-family:"comic sans ms",sans-serif"> you can recover all that energy as heating.</b></div><div style="margin-left:40px"><span style="font-family:"comic sans ms",sans-serif"></span><br><span style="font-family:"comic sans ms",sans-serif"></span><b style="font-family:"comic sans ms",sans-serif">B<i>ut if you put a bunch of energy into a system by heating, you can NOT recover all of that energy as work. </i></b></div></div><div><br></div><div>I think this is the asymmetry that requires the invention of entropy.</div><div><br></div><div>Am I finally getting my Dux in a row?</div><div><br></div><div>Nick</div><br><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" target="_blank">nthompson@clarku.edu</a></div><a href="https://wordpress.clarku.edu/nthompson" target="_blank">https://wordpress.clarku.edu/nthompson</a></div></div></div>
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