Energy Efficiency in Stochastic Processes

This proposal is framed within the field of stochastic thermodynamics, which studies energy exchanges in processes performed by mesoscale systems. Typical examples include colloidal particle systems dissolved in a solvent that can be manipulated with optical tweezers, biomolecular motors, microelectric circuits, micro-mechanical oscillators, microbial biomass, and more. Due to their small size, these systems are highly susceptible to thermal fluctuations. The variables characterizing these systems, such as positions and velocities, are stochastic processes. When these systems interact with each other, with the environment, and with external agents, energy is exchanged in the form of heat and work. However, due to fluctuations, these exchanges are also stochastic processes. The limitations imposed by the second law of classical thermodynamics apply to the average of these energy exchanges but not to specific realizations of the stochastic processes describing the system. This opens the door to exploring how thermal fluctuations influence the efficiency of energy transfers in these stochastic systems. This project aims to design control protocols for such systems that optimize the work performed and the time required for the system to reach thermal equilibrium. Additionally, it seeks to characterize the stochastic properties of the energy efficiency of these protocols. These protocols serve as the foundation for designing thermodynamic cycles for mesoscale systems in the pursuit of new alternative energy sources.