Diffusione e fluttuazioni in sistemi Browniani e multibagno

This PhD thesis concerns the study of few relevant models of nonequilibrium Statistical Mechanics. After a brief introduction to Stochastic Thermodynamics, diffusive processes and disordered systems, more detailed aspects of Large Deviations Theory, anomalous diffusion and aging dynamics are presented, related to the specific problems analyzed in the thesis. For an underdamped Brownian particle, the effect of the introduction of a harmonic potential in the large deviations function of the thermal bath work is analyzed. For the same kind of system, but in the overdamped regime, the effect of a time-changing stochastic diffusion coefficient is studied. A recently introduced class of nonequilibrium models, called multibath models, that can provide new insights into the theory of disordered systems, is also considered. For Ising-like models in this class, stationary properties and fluctuation-dissipation reations are analyzed.