Investigation on energetic optimization problems of stochastic thermodynamics with iterative dynamic programming

TL;DR

This paper explores the energetic optimization of stochastic thermodynamic systems using iterative dynamic programming, analyzing simple and multi-degree-of-freedom actuators to understand how control protocols and internal dynamics affect work efficiency.

Contribution

It introduces a numerical approach with iterative dynamic programming to optimize control protocols in stochastic thermodynamics systems, including complex multi-degree-of-freedom actuators.

Findings

Optimal control protocols differ between overdamped and underdamped systems.

Inertial effects influence irreversibility and modify optimal protocols.

Internal degrees of freedom impact the minimal input work for actuators.

Abstract

The energetic optimization problem, e.g., searching for the optimal switch- ing protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In current work, we study this problem numerically with iterative dynamic programming. The model systems under investigation are toy actuators consisting of spring-linked beads with loading force imposed on both ending beads. For the simplest case, i.e., a one-spring actuator driven by tuning the stiffness of the spring, we compare the optimal control protocol of the stiffness for both the overdamped and the underdamped situations, and discuss how inertial effects alter the irreversibility of the driven process and thus modify the optimal protocol. Then, we study the systems with multiple degrees of freedom by constructing oligomer actuators, in which the harmonic interaction between the two ending beads is tuned externally. With the same rated output work, actuators of different constructions demand different minimal input work, reflecting the influence of the internal degrees of freedom on the performance of the actuators.