Sum of exit times in a series of two metastable states
1 Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, 00161 Roma, Italy
2 Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
3 Department of Mathematics, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
Received: 1 March 2017
Published online: 19 April 2017
The problem of not degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains is considered. Metastability has been widely studied both in the mathematical and physical literature. Metastable states arises close to a first order phase transition, when the system can be trapped for a long time (exponentially long with respect to the inverse of the temperature) before switching to the thermodynamically stable phase. In this paper, under rather general conditions, we give a sharp estimate of the exit time from a metastable state in a presence of a second metastable state that must be necessarily visited by the system before eventually reaching the stable phase. In this framework we give a sharp estimate of the exit time from the metastable state at higher energy and, on the proper exponential time scale, we prove an addition rule. As an application of the theory, we study the Blume-Capel model in the zero chemical potential case.
© EDP Sciences, Springer-Verlag, 2017