Boltzmann vs Gibbs: Two Entropies, Two Uses

Philosopher of physics Wayne Myrvold reframes thermodynamics as a resource theory, arguing the slogan entropy always increases is a consequence of the second law, not the law itself, and that Gibbs and Boltzmann entropies answer different questions. We explore Maxwell's demon, Landauer erasure, free energy and fluctuations, macrostates vs microstates, disorder, ergodicity, cosmology and heat death, collapse theories, and even pedagogy and career advice. 00:00 Is entropy in the system or in our minds? 07:12 Thermodynamics as a resource theory of heat and power 18:24 Second law does not assume entropy; entropy defined by it 30:58 From caloric to molecular motion: history of entropy 39:04 Maxwell's insight: second law not absolute 48:11 Information as a resource; knowledge and entropy 1:00:53 Boltzmann vs Gibbs: different entropies, different questions 1:10:24 Maxwell's demon and Landauer's principle 1:25:02 Heat death of the universe? 1:30:19 Why equating entropy with disorder misleads 1:35:21 Ergodic hypothesis and its limited relevance 1:43:52 Statistical mechanics on shaky ground (like QFT) 1:50:50 Career advice: do not chase bandwagons Resources: - Join My New Substack (Personal Writings): https://curtjaimungal.substack.com - Ted Jacobson [TOE]: https://youtu.be/3mhctWlXyV8 - Concerning Several Conveniently Applicable Forms For The Main Equations Of The Mechanical Heat Theory [Paper]: https://web.lemoyne.edu/giunta/Clausius1865.pdf - John Norton [TOE]: https://youtu.be/Tghl6aS5A3M - On An Absolute Thermometric Scale [Paper]: https://sites.pitt.edu/~jdnorton/teaching/2559_Therm_Stat_Mech/docs/Thomson_1848.pdf - Carnot Efficiency: https://energyeducation.ca/encyclopedia/Carnot_efficiency - Maxwell's Talk On Molecules: https://victorianweb.org/science/maxwell/molecules.html - Helmholtz Free Energy: https://www.sciencedirect.com/topics/engineering/helmholtz-free-energy - Boltzmann Entropy: https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_(Smirnov_and_McCarty)/01%3A_Biochemical_Thermodynamics/1.05%3A_The_Boltzmann_Distribution_and_the_Statistical_Definition_of_Entropy - Maxwell's Letter: https://cudl.lib.cam.ac.uk/view/PH-CAVENDISH-P-00092/1 - Landauer's Principle: https://www.sciencedirect.com/science/article/abs/pii/S135521980300039X - On A Universal Tendency In Nature To The Dissipation Of Mechanical Energy: https://www.tandfonline.com/doi/abs/10.1080/14786445208647126 - Neil Turok [TOE]: https://youtu.be/zNZCa1pVE20 - Roger Penrose [TOE]: https://youtu.be/sGm505TFMbU - Sean Carroll [TOE]: https://youtu.be/9AoRxtYZrZo - Understanding The Infinite [Book]: https://www.amazon.com/Understanding-Infinite-Shaughan-Lavine/dp/0674921178 - Classical Electrodynamics [Book]: https://www.amazon.com/Classical-Electrodynamics-John-David-Jackson/dp/1119770769 - Why Information Is Entropy [YouTube]: https://youtu.be/8Uilw9t-syQ

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