  Stochastic thermostats based on the Langevin equation, in which a system is
coupled to an external heat bath, are popular methods for temperature control
in molecular dynamics simulations due to their ergodicity and their ease of
implementation. Traditionally, these thermostats suffer from sluggish behaviour
in the limit of high friction, unlike thermostats of the Nos\'e-Hoover family
whose performance degrades more gently in the strong coupling regime. We
propose a simple and easy-to-implement modification to the integration scheme
of the Langevin algorithm that addresses the fundamental source of the
overdamped behaviour of high-friction Langevin dynamics: if the action of the
thermostat causes the momentum of a particle to change direction, it is flipped
back. This fast-forward Langevin equation preserves the momentum distribution,
and so guarantees the correct equilibrium sampling. It mimics the quadratic
behavior of Nos\'e-Hoover thermostats, and displays similarly good performance
in the strong coupling limit. We test the efficiency of this scheme by applying
it to a 1-dimensional harmonic oscillator, as well as to water and
Lennard-Jones polymers. The sampling efficiency of the fast-forward Langevin
equation thermostat, measured by the correlation time of relevant system
variables, is at least as good as the traditional Langevin thermostat, and in
the overdamped regime the fast-forward thermostat performs much better,
improving the efficiency by an order of magnitude at the highest frictions we
considered.
