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Three Lectures on Metastability Under Stochastic Dynamics

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Methods of Contemporary Mathematical Statistical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1970))

Abstract

Metastability is a phenomenon where a physical, chemical or biological system, under the influence of a noisy dynamics, moves between different regions of its state space on different time scales. On short time scales the system is in a quasi-equilibrium within a single region, while on long time scales it undergoes rapid transitions between quasiequilibria in different regions (see Fig. 1).

Examples of metastability can be found in:

  • biology: folding of proteins;

  • climatology: effects of global warming;

  • economics: crashes of financial markets;

  • materials science: anomalous relaxation in disordered media;

  • physics: freezing of supercooled liquids.

The task of mathematics is to formulate microscopic models of the relevant underlying dynamics, to prove the occurrence of metastable behavior in these models on macroscopic space-time scales, and to identify the key mechanisms behind the experimentally observed universality in the metastable behavior of whole classes of systems. This is a challenging program!

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Author information

Authors and Affiliations

  1. Mathematical Institute, Leiden University, P.O. Box 9512 2300 RA 5Leiden, The Netherlands

    Frank den Hollander

  2. EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

    Frank den Hollander

Authors
  1. Frank den Hollander
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Correspondence to Frank den Hollander .

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Editors and Affiliations

  1. Ctr. for Theoretical Study, Charles University, Jilska 1, Praha 1, 110 00, Czech Republic

    Roman Kotecký

  2. Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK

    Roman Kotecký

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Hollander, F. (2009). Three Lectures on Metastability Under Stochastic Dynamics. In: Kotecký, R. (eds) Methods of Contemporary Mathematical Statistical Physics. Lecture Notes in Mathematics(), vol 1970. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92796-9_5

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