Relaxation of caloric curves on complex potential energy surfaces

Time-dependent caloric curves of model systems with complex energy landscapes are calculated by solving master equation kinetics in stepwise heating or cooling protocols. By considering in detail a simple two-state harmonic model, we show that both the transition temperature and the associated latent heat vary significantly if the sampling time is not long enough. Microcanonical characteristics, including possible S-bends in the caloric curve, are also qualitatively affected by insufficient sampling. The geometry of S-bends as a function of the observation time agrees quantitatively with the predictions of catastrophe theory. For two Lennard-Jones clusters with 13 and 31 atoms the relations between the transition temperatures and the sampling time are shown to follow scaling laws, in agreement with the results of molecular dynamics simulations [J. Chem. Phys. 113, 1315 (2000)].