Metastability is the phenomenon where a stochastic system, under the influence of a stochastic dynamics, moves between different subregions of its state space on different time scales. Metastability is encountered in a wide variety of stochastic systems, in physics, chemistry, biology and economics. The challenge is to devise realistic models and to explain the experimentally observed universality in the behaviour of metastable systems, both qualitatively and quantitatively. 

In statistical physics, metastability is the dynamical manifestation of a first-order phase transition. An example is condensation. When water vapour is cooled down slightly below 100 degrees Celsius, it persists for a very long time in a metastable vapour state before transiting to a stable liquid state under the influence of random fluctuations. The crossover occurs after the system creates a critical droplet of liquid inside the vapour, which once present grows and invades the system. While in the metastable vapour state, the system makes many unsuccessful attempts to form a critical droplet.

This lecture provides a quick panorama of questions, answers and tools around metastability, illustrated by an example that is in the frontline of current research.