随机热力学能量优化问题的迭代动态规划研究
Investigation on energetic optimization problems of stochastic thermodynamics with iterative dynamic programming
摘要：
能量优化问题，例如，随机热力学广泛研究了在系统参数一定的情况下，如何寻找最优的切换协议，使系统的输入功最小。在目前的工作中，我们研究这个问题的数值迭代动态规划。正在调查的模型系统是玩具致动器组成的弹簧连接珠与加载力施加在两端珠。对于最简单的情况，即，一个弹簧驱动器通过调整弹簧的刚度，我们比较了刚度的最优控制协议的过阻尼和欠阻尼的情况下，并讨论惯性效应如何改变驱动过程的不可逆性，从而修改最优协议。然后，我们研究了多自由度系统，通过构造寡聚物致动器，其中两个末端珠子之间的谐波相互作用是外部调谐的。在额定输出功相同的情况下，不同结构的作动器需要不同的最小输入功，反映了作动器内部自由度对作动器性能的影响。
英文摘要：
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.
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