Noise as a resource - Probing and manipulating classical and quantum dynamical systems via stochastic measurements

In this thesis, common features from the theories of open quantum systems, estimation of state dynamics and statistical mechanics have been integrated in a comprehensive framework, with the aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of specic control tasks, since it can be responsible for uncontrolled time-dependent (and even discontinuous) changes of the system. However, if the effects of the random interaction with a noisy environment are properly modeled by the introduction of a given stochasticity within the dynamics of the system, then even noise contributions might be seen as control knobs. As a matter of fact, even a partial knowledge of the environment can allow to set the system in a dynamical condition in which the response is optimized by the presence of noise sources. In particular, we have investigated what kind of measurement devices can work better in noisy dynamical regimes and studied how to maximize the resultant information via the adoption of estimation algorithms. Moreover, we have shown the optimal interplay between quantum dynamics, environmental noise and complex network topology in maximizing the energy transport efficiency. Then, foundational scientic aspects, such as the occurrence of an ergodic property for the system-environment interaction modes of a randomly perturbed quantum system or the characterization of the stochastic quantum Zeno phenomena, have been analyzed by using the predictions of the large deviation theory. Finally, the energy cost in maintaining the system in the non-equilibrium regime due to the presence of the environment is evaluated by reconstructing the corresponding thermodynamics entropy production. In conclusion, the present thesis can constitute the basis for an effective resource theory of noise, which is given by properly engineering the interaction between a dynamical (quantum or classical) system and its external environment.