  Baryon acoustic oscillation data from the first year of the Dark Energy
Spectroscopic Instrument (DESI) provide near percent-level precision of cosmic
distances in seven bins over the redshift range $z=0.1$-$4.2$. We use this
data, together with other distance probes, to constrain the cosmic expansion
history using some well-motivated physical classes of dark energy. In
particular, we explore three physics-focused behaviors of dark energy from the
equation of state and energy density perspectives: the thawing class (matching
many simple quintessence potentials), emergent class (where dark energy comes
into being recently, as in phase transition models), and mirage class (where
phenomenologically the distance to CMB last scattering is close to that from a
cosmological constant $\Lambda$ despite dark energy dynamics). All three
classes fit the data at least as well as $\Lambda$CDM, and indeed can improve
on it by $\Delta\chi^2\approx -5$ to $-17$ for the combination of DESI BAO with
CMB and supernova data, while having one more parameter. The mirage class does
essentially as well as $w_0w_a$CDM while having one less parameter. These
classes of dynamical behaviors highlight worthwhile avenues for further
exploration into the nature of dark energy.
