# Thermal dissipation and local Ohmicity of nonlinear components

In this answer, it was established that Onsager relations make a one-to-one correspondence between the linear relationship between voltage and current, and entropy creation rate in the electric component (hence, power cannot be stored even in principle, it MUST be dissipated into waste heat)

However, a potential loophole was left, as is not clear how to generalize this argument in the case where the V-I linearity exists only in a small region of currents and voltages.

Question: Is it possible in all cases to determine a relationship between rate of entropy production and the rate of current decrease with voltage decrease in a component to have the following form:

$$\frac{d S}{d t} \propto I^2 \frac{d V}{d I}$$

Do all transistors and diodes abide to such power dissipation relationship?

Draft answer: If one splits current in terms of phasor orthogonality along voltage (i.e: $$I_{\bot}$$ and $$I_{\parallel}$$) then only $$I_{\parallel}$$ contributes to increase of entropy.
$$\frac{dS}{dt} \propto I_{\parallel}^2 \Big( \frac{dI_{\parallel}}{dV} \Big)^{-1} \propto V^2 \frac{dI_{\parallel}}{dV}$$
$$\frac{dS}{dt} \propto V I_{\parallel}$$