the linear-response regime, as well as the dispersion relations of collective excitations.

Non-local Transport\[sec:Non-local-Transport\] 
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Effects of electron-hole symmetry, momentum conservation and thermal transport\[subsec:Charge-and-energy\]
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Within the kinetic approach, the charge current $\mathbf{j}_{c}$ and the heat current $\mathbf{j_{\varepsilon}}$ are given by $$\begin{aligned}
\mathbf{j}_{c} & =e\sum_{\lambda}\int_{\mathbf{k}}\lambda v\frac{\mathbf{k}}{k}f_{\mathbf{k},\lambda},\label{eq:charge_current_exp}\\
\mathbf{j_{\varepsilon}} & =\sum_{\lambda}\int_{\mathbf{k}}v^{2}\hbar\mathbf{k}f_{\mathbf{k},\lambda}.\label{eq:heat_current_exp}\end{aligned}$$ In these expressions intra-band processes that create particle-hole pairs are neglected (see Appendix \[sec:App\_Collision-operator\]). It follows from Eqs. (\[eq:charge\_current\_exp\]) (\[eq:heat\_current\_exp\]), that the even in $\lambda$ part of the distribution function $f_{\mathbf{k},\lambda}$ contains information about thermal transport, whereas the odd part governs the transport of charge. Since the electric field contribution to the kinetic equation (\[eq:Electric\_force\]) is odd in $\lambda$, and the thermal gradient leads to a term that is even in $\lambda$ (Eq. (\[eq:Thermal\_force\])), the phenomena of thermal and charge transport are decoupled to linear order in the external fields at the neutrality point. This can be traced back to particle-hole symmetry and is the ultimate reason why the Wiedemann-Franz law is dramatically violated in a Dirac fluid[@Crossno2016]. The distribution function shows a similar decoupling ocf charge and heat modes for higher $m$: The collinear modes of Eq. (\[eq:Collinear\_modes\]) are proportional to $\lambda^{m}$ for $s=1$ and to $\lambda^{m+1}$ for $s=2,3$. Consequently 