  Several methods in nonadiabatic molecular dynamics are based on Madelung's
hydrodynamic description of nuclear motion, while the electronic component is
treated as a finite-dimensional quantum system. In this context, the quantum
potential leads to severe computational challenges and one often seeks to
neglect its contribution, thereby approximating nuclear motion as classical.
The resulting model couples classical hydrodynamics for the nuclei to the
quantum motion of the electronic component, leading to the structure of a
complex fluid system. This type of mixed quantum-classical fluid models have
also appeared in solvation dynamics to describe the coupling between liquid
solvents and the quantum solute molecule. While these approaches represent a
promising direction, their mathematical structure requires a certain care. In
some cases, challenging higher-order gradients make these equations hardly
tractable. In other cases, these models are based on phase-space formulations
that suffer from well-known consistency issues. Here, we present a new complex
fluid system that resolves these difficulties. Unlike common approaches, the
current system is obtained by applying the fluid closure at the level of the
action principle of the original phase-space model. As a result, the system
inherits a Hamiltonian structure and retains energy/momentum balance. After
discussing some of its structural properties and dynamical invariants, we
illustrate the model in the case of pure-dephasing dynamics. We conclude by
presenting some invariant planar models.
