  We report a dynamic light scattering study of the fluctuation modes in a
thermotropic liquid crystalline mixture of monomer and dimer compounds that
exhibits the twist-bend nematic ($\mathrm{N_{TB}}$) phase. The results reveal a
spectrum of overdamped fluctuations that includes two nonhydrodynamic and one
hydrodynamic mode in the $\mathrm{N_{TB}}$ phase, and a single nonhydrodynamic
plus two hydrodynamic modes (the usual nematic optic axis or director
fluctuations) in the higher temperature, uniaxial nematic phase. The properties
of these fluctuations and the conditions for their observation are
comprehensively explained by a Landau-deGennes expansion of the free energy
density in terms of heliconical director and helical polarization fields that
characterize the $\mathrm{N_{TB}}$ structure, with the latter serving as the
primary order parameter. A "coarse-graining" approximation simplifies the
theoretical analysis, and enables us to demonstrate quantitative agreement
between the calculated and experimentally determined temperature dependence of
the mode relaxation rates.
