Irreversibility and nonequilibrium properties in dynamical models for turbulence and geophysical systems

Nonequilibrium phenomena display such diverse phenomenological properties that cannot be treated in a unified manner. Some of them, especially those of geophysical origin, are described by a large number of variables following complex dynamical laws, thus the need of simplified models is strongly felt. In this Thesis we aim at investigating nonequilibrium properties of two nonlinear dynamical models inspired by geophysical flows, the Lorenz96 model and the Sabra shell model, using effective tools from nonequilibrium statistical physics, namely asymmetric time correlations and response functions. We show that both indicators are able to detect the presence or absence of time irreversibility, visualize effectively the statistical fluxes where present, and ultimately provide an alternative perspective on the transport properties characterizing both systems, whether they are in- or out-of- equilibrium (namely with zero or non-zero forcing and damping, respectively).