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We derive and analyze the dynamic equations for polar liquid crystals in twospatial dimensions in the framework of classical dynamical density functionaltheory (DDFT). Translational density variations, polarization, and quadrupolarorder are used as order-parameter fields. The results are critically comparedwith those obtained using the macroscopic approach of time-dependentGinzburg-Landau (GL) equations for the analogous order-parameter fields. Wedemonstrate that for both the microscopic DDFT and the macroscopic GL approachthe resulting dissipative dynamics can be derived from a dissipation function.We obtain microscopic expressions for all diagonal contributions and for manyof the cross-coupling terms emerging from a GL approach. Thus we establish abridge between molecular correlations and macroscopic modeling for thedissipative dynamics of polar liquid crystals.

Microscopic and macroscopic theories for the dynamics of polar liquid crystals