Thermodynamic Geometry

Peter SalamonUdine Advanced School

October 2005

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

Given that something should happen,

MinSu

MaxPower

How much we care about wasting fuel

In between lies: Economics, Biology, ??

•Economics --

marginal propensity to consume power.

Industrialist vs. Environmentalist

Should the marginal propensity to consume power be the same across a well equilibrated market?

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G

Other input to production

• 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.)

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

Minimum Dissipation

• Measured by lost exergy or by entropy produced.– Gouy-Stodola

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T 0ΔSu = −ΔAu ≥ 0

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.

Coffee Cup Motel

…

T0 T1Tn

Entropy production is a small equilibration

Exercise

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Su ≥ L2 /2K

What does distance measure?

• Velocity -- shock tube

• dL2 = dissipation in a small equilibration

• Fluctuation

"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.