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We study the conductivities $\sigma$ of (i) the equilibrium isochoric state($\sigma_{\rm is}$), (ii) the equilibrium isobaric state ($\sigma_{\rm ib}$),and also the (iii) non-equilibrium ultrafast matter (UFM) state ($\sigma_{\rmuf}$) with the ion temperature $T_i$ less than the the electron temperature$T_e$. Aluminum, lithium and carbon are considered, being increasingly complexwarm dense matter (WDM) systems, with carbon having transient covalent bonds.First-principles calculations, i.e., neutral-pseudoatom (NPA) calculations anddensity-functional theory (DFT) with molecular-dynamics (MD) simulations, arecompared where possible with experimental data to characterize $\sigma_{\rmic}, \sigma_{\rm ib}$ and $\sigma_{\rm uf}$. The NPA $\sigma_{\rm ib}$ areclosest to the available experimental data when compared to results fromDFT+MD, where simulations of about 64-125 atoms are typically used. Thepublished conductivities for Li are reviewed and the value at a temperature of4.5 eV is examined using supporting X-ray Thomson scattering calculations. Aphysical picture of the variations of $\sigma$ with temperature and densityapplicable to these materials is given. The insensitivity of $\sigma$ to $T_e$below 10 eV for carbon, compared to Al and Li, is clarified.

Isochoric, isobaric and ultrafast conductivities of aluminum, lithium and carbon in the warm dense matter (WDM) regime