USask Mathematics & Statistics Colloquium: Lamberto Rondoni

The microscopic theory of equilibrium phenomena is highly developed and rather exhaustive, while that of non-equilibrium phenomena still faces fundamental challenges and lacks a unitary formulation, although both the equilibrium and the non-equilibrium theories were born together. One may argue that this is due to the fact that every equilibrium state can be perturbed in many possible ways, making it a non-equilibrium state, hence non-equilibrium states constitute a much wider class than that of equilibrium phenomena. The available mathematical techniques, concern dynamical systems and stochastic processes, and include ergodic theory, linear response theory and fluctuation theorems, which have been successfully and widely applied in science and technology. Recently, a non-perturbative, exact response theory has emerged within the framework of molecular dynamics and fluctuations theorems. We are going to briefly mention some of the numerous applications of this theory, that starts with (deterministic) dynamical systems, and is now gradually developing in view of applications to stochastic processes and to quantum mechanics.