1. Thermodynamic Geometry Peter Salamon Udine Advanced School October 2005

2. Finite Time Thermodynamics 3 (at least) Big Questions –Maximum power –Minimum dissipation –Thermodynamic waiting time Number of fluctuations 1 (at least) Big Failing –No contact with experiment

3. Given that something should happen, Min  S u Max Power How much we care about wasting fuel In between lies: Economics, Biology, ??

4. Economics --  marginal propensity to consume power.  Industrialist vs. Environmentalist  Should the marginal propensity to consume power be the same across a well equilibrated market? Other input to production

5. Biology Examples --  Is there a lion chasing me?  What degree of flagellar stirring should I do to get the most food (O2). Degree of multicellularity as a function of Peclet number. (Ray Goldstein, U. of Ariz.)

6. Finite Time Thermodynamics 3 (at least) Big Questions –Maximum power –Minimum dissipation –Thermodynamic waiting time 1 (at least) Big Failing –No contact with experiment Endoreversible Geometry Untried One sad story in second lecture

7. Minimum Dissipation Measured by lost exergy or by entropy produced. –Gouy-Stodola

8. Basic physical problem: How much entropy must be produced to bring a system along a given sequence of states? Example: Heat a cup of coffee.

9. Coffee Cup Motel

10. … T0T0 T1T1 TnTn Entropy production is a small equilibration

11. Exercise

13. What does distance measure? Velocity -- shock tube dL 2 = dissipation in a small equilibration Fluctuation

16. "Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown." — Albert Einstein Thermodynamics is almost mathematics.