We investigate a Geometric Brownian Information Engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into extractable work. Outcomes of the information engine depend on the reference measurement distance $x_m$, feedback site $x_f$ and the transverse force $G$. We determine the benchmarks for utilizing the available information in an output work and the optimum operating requisites for best work extraction. Transverse bias force ($G$) tunes the entropic contribution in the effective potential and hence the standard deviation ($\sigma$) of the equilibrium marginal probability distribution. We recognize that the amount of extracted work reaches a global maximum when $x_f = 2x_m$ with $x_m \sim 0.6\sigma$, irrespective of the extent of the entropic limitation. Because of the higher loss of information during the relaxation process, the best achievable work of a GBIE is lower in an entropic system. The feedback regulation also bears the unidirectional passage of particles. The average displacement increases with growing entropic control and is maximum when $x_m \sim 0.81\sigma$. Finally, we explore the efficacy of the information engine, a quantity that regulates the efficiency in utilizing the information acquired. With $x_f=2x_m$, the maximum efficacy reduces with increasing entropic control and shows a cross over from $2$ to $11/9$. We discover that the condition for the best efficacy depends only on the confinement length scale along the feedback direction. The broader marginal probability distribution accredits the increased average displacement in a cycle and the lower efficacy in an entropy-dominated system.

中文翻译：

---

几何布朗信息引擎：获得最佳性能的必要条件

我们在存在无误差反馈控制器的情况下研究几何布朗信息引擎 (GBIE)，该控制器将收集到的关于陷入单叶几何约束的布朗粒子状态的信息转换为可提取的工作。信息引擎的结果取决于参考测量距离 $x_m$、反馈位置 $x_f$ 和横向力 $G$。我们确定了在输出工作中利用可用信息的基准以及最佳工作提取的最佳操作要求。横向偏置力 ($G$) 调整有效势中的熵贡献，从而调整平衡边际概率分布的标准偏差 ($\sigma$)。我们认识到，当 $x_f = 2x_m$ 且 $x_m \sim 0.6\sigma$ 时，提取的工作量达到全局最大值，与熵限制的程度无关。由于松弛过程中的信息损失较高，GBIE 的最佳可实现工作在熵系统中较低。反馈调节也承载着粒子的单向通过。平均位移随着熵控制的增加而增加，并且在 $x_m \sim 0.81\sigma$ 时最大。最后，我们探讨了信息引擎的功效，这是一个调节利用所获得信息的效率的量。当 $x_f=2x_m$ 时，最大功效随着熵控制的增加而降低，并显示出从 $2$ 到 $11/9$ 的交叉。我们发现最佳功效的条件仅取决于沿反馈方向的限制长度尺度。