In order to understand the behavior of thermodynamic quantities near the glass transition temperature, we put the energy landscape picture and the particle’s jump motion together and calculate the specific heat of a nonequilibrium system. Taking the finite observation time into account, we study the observation time dependence of the specific heat. We assume the Einstein oscillators for the dynamics of each basin in the landscape structure of phase space and calculate the specific heat of a system with 20 basins. For a given observation time, a transition from annealed to quenched system occurs at the temperature when the time scale of jumps exceeds the observation time. The transition occurs at lower temperature and becomes sharper for longer observation time. © 2002 The American Physical Society.