Metastability for General Dynamics with Rare Transitions: Escape Time and Critical Configurations

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an el...

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Bibliographic Details
Published in:Journal of statistical physics 2015-10, Vol.161 (2), p.365-403
Main Authors: Cirillo, Emilio N. M., Nardi, Francesca R., Sohier, Julien
Format: Article
Language:English
Subjects:
Markov processes
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical content, we believe that our results are a useful tool to approach metastability for non-Metropolis systems such as Probabilistic Cellular Automata.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1334-6