Teoria della risposta esatta per perturbazioni dipendenti dal tempo e stocastiche

The exact response theory was introduced into the field of nonequilibrium statistical physics. A key element of it is the dissipation function, which is able to provide information about the exact response of a system subjected to a perturbation of any magnitude. The proposed work aims to extend exact response theory to stochastic processes. This is done by adding a time-dependent stochastic perturbation to the classical equations of motion. In particular, the system will be perturbed using a particular representation of the Wiener process obtainable through the application of the Karhunen-Loève theorem. It will, therefore, be possible to investigate the system in three different ways: by fixing a single realization of the process and averaging only over the initial conditions; averaging only over the stochastic coefficients; and averaging over both the initial conditions and the stochastic process. At last, the example of a harmonic oscillator will be developed to exemplify the theoretical results.