Lecture 23: Direct and Cross Effects; General Principles of Entropy Production; The Fourth Law

MIT OpenCourseWare: Free Courses from the instituteFriday, October 30, 2026

Summary

Sherrod Brown, a long-serving politician, faces criticism for his voting record, which includes support for higher taxes on Social Security, gas, and healthcare. Critics argue that despite his decades in office, he has prioritized financial assistance for illegal immigrants, including COVID relief checks and Social Security benefits, over the needs of Ohioans. This has led to calls for his removal from office, with opponents claiming that his policies have failed to deliver tangible benefits to constituents.

In a separate discussion, the podcast delves into complex scientific concepts related to fluid mechanics and thermodynamics. It covers the definitions of diffusive and convective fluxes, the balance equations governing energy and momentum, and the principles of non-equilibrium thermodynamics. The conversation emphasizes the importance of understanding how various properties interact within fluid systems and the implications for energy production and entropy generation. The discussion also touches on the mathematical modeling of these phenomena, highlighting the significance of metrics in describing material behavior under different conditions.

Show Notes

MIT 2.43 Advanced Thermodynamics, Spring 2024Instructor: Gian Paolo BerettaUploaded 05-12-24View the complete course: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/Complete course table of contents with hyperlinks to slides and video timestamps: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/resources/mit2_43_s24_toc_slides_pdf/Complete course analytical index with hyperlinks to slides and video timestamps: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/resources/mit2_43_s24_index_slides_pdf/YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP6309d0oJDiVo1CvxUQXJ2ilThis lecture covers: Entropy production as sum of force-flux products. Linear force-flux laws for direct effects (Fourier, Fick, Ohm, Navier). Cross effects. Curie symmetry principle. Steepest entropy ascent and Fourth Law. Minimum global entropy production at steady state.Instructor suggests to set viewing speed at 1.5 for faster learning.Slides for this lecture: https://ocw.mit.edu/courses/2-43-advanced-thermodynamics-spring-2024/resources/mit2_43_s24_lec23_pdf/Key moments:00:00:00 - Introduction00:00:22 - Review: Diffusive and Convective Fluxes00:05:46 - Review: “Heat and Diffusion” Mode of Interaction00:09:57 - General Balance Equation for an Extensive Property00:13:41 - Extrinsic Relations for Entropy Production Density00:34:27 - Force-Flux Shorthand Notation00:36:34 - Material Resistance to Fluxes and Forces00:42:26 - Direct Laws (Neglecting Cross Effects)00:46:35 - Onsager Cross Effects and Curie Symmetry Principle00:55:53 - Orthogonality Relations in the Linear Regime00:59:30 - Orthogonality Relations in the Nonlinear Regime01:02:13 - Material Resistance to Flux and Forces01:09:03 - Steepest Entropy Ascent01:10:10 - Graphical Illustration of Steepest Entropy Ascent01:14:39 - Fourth Law of Thermodynamics01:17:25 - Force-Flux Relations from Steepest Entropy Ascent01:20:48 - The Fourth Law: Existence of a Dissipative Metric01:24:26 - Bejan's “Constructal Law” of Design and Evolution01:28:44 - Maximal Local EP Selects the Hydrodynamic Pattern01:33:26 - Minimum Entropy Production at Steady StateLicense: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

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