  Quasi-equilibrium relaxational thermodynamics is developed to understand
LA-phonon-assisted thermalization of Bose-Einstein distributed excitons in
quantum wells. We study the quantum-statistical effects in the relaxational
dynamics of the effective temperature of excitons $T = T(t)$. When $T$ is less
than the degeneracy temperature $T_0$, well-developed Bose-Einstein statistics
of quantum well excitons leads to nonexponential and density-dependent
thermalization. At low bath temperatures $T_b \to 0$ the thermalization of
quantum-statistically degenerate excitons effectively slows down and $T(t)
\propto 1 / \ln t$. We also analyze the optical decay of Bose-Einstein
distributed excitons in perfect quantum wells and show how nonclassical
statistics influences the effective lifetime $\tau_{opt}$. In particular,
$\tau_{opt}$ of a strongly degenerate gas of excitons is given by $2 \tau_R$,
where $\tau_R$ is the intrinsic radiative lifetime of quasi-two-dimensional
excitons. Kinetics of resonant photoluminescence of quantum well excitons
during their thermalization is studied within the thermodynamic approach and
taking into account Bose-Einstein statistics. We find density-dependent
photoluminescence dynamics of statistically degenerate excitons. Numerical
modeling of the thermalization and photoluminescence kinetics of
quasi-two-dimensional excitons are given for GaAs/AlGaAs quantum wells.
