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We will present recent works which aim at understanding the mathematical foundations of first order kinetics and the harmonic transition state theory. The cornerstone of the analysis is the notion of quasi stationary distribution. This analysis sheds a new light on the accelerated molecular dynamics algorithms which have been proposed by Arthur Voter and co-workers in the late nineties. It also opens the route to generalizations of the original algorithms, in particular of the Parallel Replica algorithm. Host: Danny Perez |