<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"></head><body dir="auto">Quanta Magazine recently had a nice illustration of entropy <div dir="auto">https://www.quantamagazine.org/what-is-entropy-a-measure-of-just-how-little-we-really-know-20241213/</div><div dir="auto"><br></div><div dir="auto">I would say addition of heat increases disorder/entropy in general because in a typical thermodynamic system which is isolated from the environment </div><div dir="auto"> * Heat increases the kinetic energy of particles which start to move faster</div><div dir="auto"> * Faster movement leads to more collisions and diverging paths. In effect this means <span style="color: rgb(32, 33, 34); font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Inter, Helvetica, Arial, sans-serif; font-size: 16px; background-color: rgb(255, 255, 255);">small changes in one state of the system </span><span style="color: rgb(32, 33, 34); font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Inter, Helvetica, Arial, sans-serif; font-size: 16px; background-color: rgb(255, 255, 255);">can result in large differences in later states, i.e. to </span>random motion</div><div dir="auto"> * More random motion increases the disorder/entropy of the system</div><div dir="auto"><br></div><div dir="auto">-J.</div><div dir="auto"><br></div><div><br></div><div align="left" dir="auto" style="font-size:100%;color:#000000"><div>-------- Original message --------</div><div>From: Nicholas Thompson <thompnickson2@gmail.com> </div><div>Date: 12/29/24 12:15 AM (GMT+01:00) </div><div>To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> </div><div>Subject: [FRIAM] Boltzmann Distribution </div><div><br></div></div><div dir="ltr"><div>FWIW, I have been struggling with the concept of entropy for the last month. One of the puzzles was why entropy increased with addition of heat. I bullied George for a few hours and he finally admitted not only that the mean and variance of the B-distribution are correlated, but that its variance is the square of its mean. Why that is the case is beyond both of us.<br></div><div><br></div><div>He also coughed up eventually the reason that adiabatic compression and decompression don't alter entropy: there is a trade off between spatial constraint and kinetic energy such that as the gas is confined its kinetic energy goes up and with that a compensating increase in the variance of the KE. <br></div><div><br></div><div>Yeah. I know. Fools rush in where wise men fear to tread. <br></div><div><br></div><div>N<br clear="all"></div><br><span class="gmail_signature_prefix">-- </span><br><div data-smartmail="gmail_signature" class="gmail_signature" 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">nthompson@clarku.edu</a></div><a href="https://wordpress.clarku.edu/nthompson">https://wordpress.clarku.edu/nthompson</a></div></div></div>
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