The life-time of nonequilibrium metastable states

In physical systems subject to thermal noise and conservative forces, metastable states are free energy minima enclosed by high barriers, whose life-time is given by the Kramers-Arrhenius formula. In systems that evolve far from equilibrium, states that are barely populated at equilibrium can be stabilized by the action of nonconservative forces and turned into metastable states: there exists in general no relation, akin to Kramers-Arrhenius formula, between free energy and the life-time of such states. The thesis aims to critically assess recent bounds on the life-time of nonequilibrium metastable states in terms of the energy dissipated by the nonconservative forces. The analytic work will focus on the analysis of the problem by means of the theory of large deviations and nonequilibrium response. Numerical simulations will be employed to test the domain of validity of the result in the specific model of a Brownian particle in a double well potential under shear flow.