Stochastic Time-Dependent Current-Density-Functional Theory

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state $|{\Psi }_0⟩$ and the particle-bath interaction operator, two external vector potentials $\mathbf{A}(\mathbf{r},t)$ and ${\mathbf{A}}^{\prime }(\mathbf{r},t)$ that produce the same ensemble-averaged current density, $\overline{\mathbf{j}(\mathbf{r},t)}$, must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.