This thesis investigates the nonequilibrium dynamics of a variety of systems evolving under control protocols. A control protocol can involve feedback based on measurements performed by an external agent, or it can be a predefined protocol that does not rely on explicit measurements of the system’s state. In the context of information thermodynamics, the former setup belongs to the paradigm of non-autonomous or feedback-controlled Maxwell’s demons, and the latter to the paradigm of autonomous demons.
The thesis begins with a framework for analyzing non-autonomous feedback control, when the control protocol is applied by an agent making continuous measurements on the system. A multiple-timescales perturbation theory, applicable when there exists an appropriate separation of timescales, is developed. This framework is applied to a classical two-state toy model of an information engine – a device that uses feedback control of thermal fluctuations to convert heat into work. Additionally, quantum trajectory simulations are used to study a feedback-controlled model of Maxwell’s demon in a double quantum dot system.
Next, a modeling scheme for converting feedback-controlled Maxwell’s demons to au- tonomous (non-feedback) systems is developed. This scheme explicitly accounts for the thermo- dynamic costs of information processing, by incorporating an information reservoir, modeled as a sequence of bits. This modeling scheme is then applied for converting the classical analogue of the non-autonomous double quantum dot Maxwell’s demon, discussed previously, to an au- tonomous model. Using analytical, semi-analytical and stochastic simulation-based approaches, it is shown that the obtained model can act either as an information engine, or as a “Landauer eraser”, and then the phase diagrams that identify these regimes of behavior are constructed.
Finally, fast-forward shortcuts to adiabaticity for classical Floquet-Hamiltonian systems is developed, and applied to a periodically driven asymmetric double well (without feedback control). Tools from dynamical systems theory are then used to characterize the system’s angle- variable dynamics.