Performance of optimal linear-response processes in driven Brownian motion far from equilibrium

Optimal work fluctuations for finite-time and weak processes

The optimal protocols for the irreversible work achieve their maximum usefulness if their work fluctuations are the smallest ones. In this work, for classical and isothermal processes subjected to finite-time and weak drivings, I show that the optimal protocol for the irreversible work is the same for the variance of work. This conclusion is based on the fluctuation-dissipation relation W[over ¯]=ΔF+βσ_{W}^{2}/2, extended now to finite-time and weak drivings. To illustrate it, I analyze a white-noise overdamped Brownian motion subjected to an anharmonic stiffening trap for fast processes. By contrast with the already known results in the literature for classical systems, the linear-response theory approach of the work probabilistic distribution is not a Gaussian reduction.

Global optimization and monotonicity in entropy production of weak drivings

Knowing if an optimal solution is local or global has always been a hard question to answer in more sophisticated situations of optimization problems. In this paper, for finite-time and weak isothermal driving processes, we show the existence of a global optimal protocol for the entropy production. We prove this by showing its convexity as a functional in the derivative of the protocol. This property also proves its monotonicity in such a context, which leads to the satisfaction of the second law of thermodynamics. In the end, we exemplify that the analytical technique of the Euler-Lagrange equation applied to overdamped Brownian motion delivers the global optimal protocol, by comparing it with the results of the global optimization technique of genetic programming.