  Stochastic Langevin dynamics has been traditionally used as a tool to
describe non-equilibrium processes. When utilized in systems with collective
modes, traditional Langevin dynamics relaxes all modes indiscriminately,
regardless of their wavelength. We propose a generalization of Langevin
dynamics that can capture a differential coupling between collective modes and
the bath, by introducing spatial correlations in the random forces. This allows
modeling the electronic subsystem in a metal as a generalized Langevin bath
endowed with a concept of locality, greatly improving the capabilities of the
two-temperature model. The specific form proposed here for the spatial
correlations produces physical wavevector- and polarization-dependency of the
relaxation produced by the electron-phonon coupling in a solid. We show that
the resulting model can be used for describing the path to equilibration of
ions and electrons, and also as a thermostat to sample the equilibrium
canonical ensemble. By extension, the family of models presented here can be
applied in general to any dense system, solids, alloys and dense plasmas. As an
example, we apply the model to study the non-equilibrium dynamics of an
electron-ion two-temperature Ni crystal.
