Capacitor - Inductor duality

We must look for a new effect in which, the energy of a capacitor/inductor, instead of 

$$E=\frac{1}{2}CV^2,$$ $$E=\frac{1}{2}LI^2,$$ 

is given by 

$$E \propto \dot{I},$$ $$E \propto \dot{V}.$$

This can only happen with AC currents. 

Pure Semiconductors

 $$E=q\varphi$$

$$q=\pm e$$

$$Z_1=e^{\beta e\varphi}+e^{-\beta e\varphi}$$

Indistinguishability ≡ Interaction

 $$Z_N=Z_1^N$$

$$Z_N=\prod_i Z_i$$

$$\prod_i \frac{Z_i}{i}=\frac{Z_1^N}{N!}$$