Sum of exit times in a series of two metastable states
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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.
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- 3.E. Olivieri, M.E. Vares, Large deviations and metastability (Cambridge University Press, UK, 2004)Google Scholar
- 6.A. Bovier, F. den Hollander, Metastability: a potential–theoretic approach (Grundlehren der mathematischen Wissenschaften, Springer, 2015)Google Scholar
- 7.M. Slowik, Metastability in Stochastic Dynamics: Contributions to the Potential Theoretic Approach (Südwestdeutscher Verlag für Hochschulschriften, 2012)Google Scholar
- 17.E.N.M. Cirillo, F.R. Nardi, C. Spitoni, Sum of exit times in a series of two metastable states in Probabilistic Cellular Automata, in Cellular Automata and Discrete Complex Systems, 22nd IFIP WG 1.5 International Workshop, AUTOMATA 2016, Zurich, Switzerland, June 15, 2016, Proceedings (Springer, 2016)Google Scholar
- 18.O. Catoni, Simulated annealing algorithms and Markov chains with rare transitions, in Séminaire de Probabilités, XXXIII, Vol. 1709 of Lecture Notes in Math. (Springer, Berlin, 1999), p. 69Google Scholar
- 22.A. Bovier, Metastability: a potential theoretic approach, in Proceedings of ICM 2006 (EMS Publishing House, 2006), p. 499Google Scholar
- 23.A. Gaudillière, Condenser physics applied to Markov Chains, in XII Escola Brasileira de Probabilidade, Ouro Preto (Minas Gerais, Brazil, 2008)Google Scholar