  The thermodynamic uncertainty relation (TUR) quantifies a relationship
between current fluctuations and dissipation in out-of-equilibrium overdamped
Langevin dynamics, making it a natural counterpart of the
fluctuation-dissipation theorem in equilibrium statistical mechanics. For
underdamped Langevin dynamics, the situation is known to be more complicated,
with dynamical activity also playing a role in limiting the magnitude of
current fluctuations. Progress on those underdamped TUR-like bounds has largely
come from applications of the information-theoretic Cram\'er-Rao inequality.
Here, we present an alternative perspective by employing large deviation
theory. The approach offers a general, unified treatment of TUR-like bounds for
both overdamped and underdamped Langevin dynamics built upon current
fluctuations achieved by scaling time. The bounds we derive following this
approach are similar to known results but with differences we discuss and
rationalize.
