  Compact-object binaries including a white dwarf component are unique among
gravitational-wave sources because their evolution is governed not just by
general relativity and tides, but also by mass transfer. While the black hole
and neutron star binaries observed with ground-based gravitational-wave
detectors are driven to inspiral due to the emission of gravitational
radiation--manifesting as a "chirp-like" gravitational-wave signal--the
astrophysical processes at work in double white dwarf (DWD) systems can cause
the inspiral to stall and even reverse into an outspiral. The dynamics of the
DWD outspiral thus encode information about tides, which tell us about the
behaviour of electron-degenerate matter. We carry out a population study to
determine the effect of the strength of tides on the distributions of the DWD
binary parameters that the Laser Interferometer Space Antenna (LISA) will be
able to constrain. We find that the strength of tidal coupling parameterized
via the tidal synchronization timescale at the onset of mass transfer affects
the distribution of gravitational-wave frequencies and frequency derivatives
for detectably mass-transferring DWD systems. Using a hierarchical Bayesian
framework informed by binary population synthesis simulations, we demonstrate
how this parameter can be inferred using LISA observations. By measuring the
population properties of DWDs, LISA will be able to probe the behavior of
electron-degenerate matter.
