标题： 具有有限循环时间的几何布朗信息引擎：输出功、功率和效率的优化 显示英文标题

标题： Geometric Brownian information engine with finite cycle time: Optimisation of output work, power and efficiency

摘要： 我们研究了一个几何布朗信息引擎，探讨有限循环时间$(\tau)$对可提取功、功率和效率的影响。 我们引入了一个无错误反馈控制器，该控制器将关于受限于二维单层几何结构中的过阻尼布朗粒子状态的信息转化为可提取的功。 信息引擎的性能取决于循环周期$(\tau)$、测量距离$(x_m)$和控制器的反馈位置$(x_f)$。 当反馈循环时间增加时，引擎从高非平衡稳态过渡到完全松弛的状态。 我们将测量距离设定在一个与完全松弛状态相关的最佳位置（$x_m^* \sim 0.6 \sigma$）。 当循环时间为有限且较短（$\tau <\tau_r$）时，反馈位点的较短距离能实现最佳的信息处理。 当循环时间增加到完全松弛状态（$\tau \gg \tau_r$）时，如预期的那样，在反馈位置处可实现的最大可提取功被设定为$x_m^*$的两倍。 当循环时间（$\tau$）长于松弛时间（$\tau_r$）时，当归一化的反馈位置正好是最佳测量距离（$x_f^{*}=2x_m^*$）的两倍时，可达到最大功率。 相反，当$\tau < \tau_r$时，当反馈点设置在一个较低的值时，可以实现最大功率。 随着$\tau$的增加，最大平均功率减小。 在长$\tau$极限下，当$x_f$位于$2x_m$时可达到最高的效率和可提取功，与熵控制的水平无关。 随着熵控制优势的增加，由于弛豫过程中的信息损失增加，在完全弛豫状态下可提取功和效率降低。 显示英文摘要

摘要： We consider a Geometric Brownian Information Engine to explore the effects of finite cycle time $(\tau)$ on the extractable work, power, and efficiency. We incorporate an error-free feedback controller that converts the information obtained about the state of overdamped Brownian particles, confined within a 2-D monolobal geometry, into extractable work. The performance of the information engine depends on the cycle period $(\tau)$, measurement distance $(x_m)$, and feedback location $(x_f)$ of the controller. Upon increasing the feedback cycle time, the engine transitions from a high non-equilibrium steady state to a completely relaxed state. We set the measurement distance at an optimum position related to a fully relaxed state ($x_m^* \sim 0.6 \sigma$). When the cycle time is finite and short ($\tau <\tau_r$), the best information processing occurs with a shorter distance of the feedback site. While increasing the cycle time towards a fully relaxed state ($\tau \gg \tau_r$), the maximum extractable work that can be achieved with a feedback location is set to be twice that of $x_m^*$, as expected. When the cycle time ($\tau$) is longer than the relaxation time ($\tau_r$), the maximum power is achieved when the scaled feedback location is exactly double the optimum measurement distance ($x_f^{*}=2x_m^*$). In contrast, when $\tau < \tau_r$, the maximum power is achieved when the feedback site is set at a lower value. As the $\tau$ increases, the maximum average power decreases. In the limit of a long $\tau$, the highest efficiency as well extractable work is attained when $x_f$ is located at $2x_m$, regardless of the level of entropic control. As the dominance of entropic control increases, the extractable work and efficiency in the fully relaxed state decrease due to higher information loss during relaxation.