Investigation on Energetic Optimization Problems of Stochastic Thermodynamics with Iterative Dynamic Programming (Communications in Computational Physics, 2010)
The energetic optimization problem, e.g., searching for the optimal switchingprotocol of certain system parameters to minimize the input work, has been extensivelystudied by stochastic thermodynamics. In this work, we study this problemnumerically using iterative dynamic programming. The model systems under investigationare toy actuators consisting of spring-linked beads with loading force imposedon both ending beads. For the simplest case, i.e., a one-spring actuator driven by tuningthe stiffness of the spring, we compare the optimal control protocol of the stiffnessfor both the overdamped and the underdamped situations, and discuss how inertialeffects alter the irreversibility of the driven process and thus modify the optimal protocol.Then, we study the systems with multiple degrees of freedom by constructingoligomer actuators, in which the harmonic interaction between the two ending beads istuned externally. With the same rated output work, actuators of different constructionsdemand different minimal input work, reflecting the influence of the internal degreesof freedom on the performance of the actuators.