We propose a general framework of calculating the specific heat of the syst
em in nonequilibrium, where the dynamics of the representative point can be
separated into fast motion in a basin of energy landscape and the slow sto
chastic jump motion among basins. We apply this framework to gaseous hydrog
en and obtain the observation time (t(obs)) dependence of the specific heat
. We find that the specific heat gives the quenched and the annealed one in
the limit of t(obs)-->0 and t(obs)--> infinity, respectively. We also inve
stigate the waiting time and the observation time dependence of the specifi
c heat and show that, for shorter waiting time, the observation time must b
e Ion-er to obtain the same degree of annealing. This tendency is consisten
t with the observation that the glass transition temperature is higher for
faster quenching.