Quantization and Cohomology (Week 13)
Posted by John Baez
This week in our course on Quantization and Cohomology, we saw how statistical mechanics involves a number system $\mathbb{R}^T$ that depends on the temperature $T$. In the ‘chilly limit’ $T \to 0$, this reduces to the number system $\mathbb{R}^{min}$ suitable for classical statics, where energy is minimized:

Week 13 (Feb. 6)  Statistical mechanics
and deformation of rigs. Statistical mechanics (or better, ‘thermal
statics’) as matrix mechanics over a rig $\mathbb{R}^T$ that depends on
the temperature T.
As T → 0, the rig $\mathbb{R}^T$ reduces to $\mathbb{R}^{min}$ and
thermal statics reduces to classical statics, just as
quantum dynamics reduces to classical dynamics as Planck’s constant
approaches zero.
Tropical mathematics, idempotent analysis and Maslov dequantization.
 Supplementary reading: G. L. Litvinov, The Maslov dequantization, idempotent and tropical mathematics: a brief introduction.
Last week’s notes are here.
Posted at February 6, 2007 8:51 PM UTC
Re: Quantization and Cohomology (Week 13)
So to reask my questions:
Where does quantum thermodynamics fit in? Is it that there’s a statistical mechanics for each complex number, the real part corresponding to temperature, and the complex part the value of $\hbar$? Or aren’t the parameters between which Wick rotation acts able to be related like that?