Using the maximum entropy principle, we present a general theory to describe ac and dc high-field transport in monolayer graphene within a dynamical context. Accordingly, we construct a closed set of hydrodynamic (HD) equations containing the same scattering mechanisms used in standard Monte Carlo (MC) approaches. The effects imputable to a linear band structure, the role of conductivity effective mass of carriers, and their connection with the coupling between the driving field and the dissipation phenomena are analyzed both qualitatively and quantitatively for different electron densities. The theoretical approach is validated by comparing HD results with existing MC simulations.
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