  We show that the stellar surface-brightness profiles in disc
galaxies---observed to be approximately exponential---can be explained if
radial migration efficiently scrambles the individual stars' angular momenta
while conserving the circularity of the orbits and the total mass and angular
momentum. In this case the disc's distribution of specific angular momenta $j$
should be near a maximum-entropy state and therefore approximately exponential,
$dN\propto\exp(-j/\langle j\rangle)dj$. This distribution translates to a
surface-density profile that is generally not an exponential function of
radius: $\Sigma(R)\propto\exp[-R/R_e(R)]/(RR_e(R))(1+d\log v_c(R)/d\log R)$,
for a rotation curve $v_c(R)$ and $R_e(R)\equiv\langle j\rangle/v_c(R)$. We
show that such a profile matches the observed surface-brightness profiles of
disc-dominated galaxies as well as the empirical exponential profile. Disc
galaxies that exhibit population gradients cannot have fully reached a
maximum-entropy state but appear to be close enough that their
surface-brightness profiles are well-fit by this idealized model.
