Definition 0.1.1 The temperature gradient denoted $\vec{\nabla} T(\vec{r})$ is the the gradient of temperature $T(\vec{r})$ at position $\vec{r}$ in a material.
Definition 0.1.2 The heat current denoted $\vec{j}_q$ is the rate of energy transfer through a material due to temperature gradient.
Definition 0.1.3 The thermal conductivity denoted $k$ of a material is the coefficient that relates the temperature gradient $\nabla T$ to the heat current $\vec{j}_q$.
\[\vec{j}_q = -k\sigma \vec{E}\]
Definition 0.1.4
Definition 0.1.5
Result 0.1.6
Result 0.1.7
Result 0.1.8
Result 0.1.9
Result 0.1.10
Definition 0.1.11 \[\text{DYNAMIC EQUATION}\]\[\text{Equilibrium Condition}\]
Definition 0.1.12 linear response coefficients
Result 0.1.13 electric conductivity, heat conductivity, seabeck
Result 0.1.14 Drude-Lorentz Heat capacity
Definition 0.1.15 The Lorentz number denoted $L$ is the proportionality constant that relates the thermal conductivity $\kappa$ to the electric conductivity $\sigma$ at temperature $T$.
\[L = \frac{\kappa}{\sigma T}\]
Law 0.1.16 The Wiedemann–Franz law states that the Lorentz number $L$ is a constant that can be written in terms of the Boltzmann constant $k_B$ and the elementary charge $e$.
\[L = \frac{\kappa}{\sigma L} = \frac{\pi^2}{3}\left( \frac{k_B}{e} \right)^2\]