Fascinating phenomena emerge from the appearance of far-from-equilibrium thermodynamic states, from active matter to protein folding dynamics, including non-trivial heat flows. Nevertheless, the complexity of these phenomena makes their fundamental understanding difficult. In this context, the FENNEC project aims at investigating experimentally and theoretically far-from-equilibrium nanothermodynamics through the careful engineering of colored heat baths of an optically levitated particle. First, it proposes to develop experimental and theoretical tools to generate and characterize out-of-equilibrium dynamics of the systems. Then, it addresses the stochastic energetics of the particle in controlled out-of-equilibrium states or during state-to-state transformations, introducing protocols that could improve and optimize such transformations. Finally, it proposes to take advantage of the out-of-equilibrium system dynamics to investigate and improve the efficiency of heat and particle transport. The FENNEC project will thus provide a unique experimental platform associated with innovative theoretical frameworks for studying far-from-equilibrium systems associated with colored heat baths. It will pave the way for developing efficient nanosystems for transport and sensing.