  For the dynamical glassy transition in the $p$-spin mean field spin glass
model a thermodynamic description is given. The often considered marginal
states are not the relevant ones for this purpose. This leads to consider a
cooling experiment on exponential timescales, where lower states are accessed.
The very slow configurational modes are at quasi-equilibrium at an effective
temperature. A system independent law is derived that expresses their
contribution to the specific heat. $t/t_w$-scaling in the aging regime of
two-time quantities is explained.
