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arXiv 2412.09802cond-mat.stat-mech
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单自旋热机的功率与效率优化

Optimizing power and efficiency of a single spin heat engine

Rita Majumdar, Monojit Chatterjee, Rahul Marathe

AI总结:

本研究基于Glauber动力学构建单自旋热机模型,推导长时间极限下的性能解析表达式,通过梯度下降和变分原理优化热机的效率与功率,证实变分方法优化效果更优。

摘要:

我们利用Glauber动力学研究了时变磁场下单自旋的行为。通过按照特定协议改变磁场,我们将该系统设计为可发挥热机功能。随后,我们采用多种协议并借助随机热力学分析该热机的性能,计算用于量化热机性能的关键物理量的平均值。在热机循环的长时间极限下,我们推导得出了广义协议下功、热量和效率的精确解析表达式。接着,我们从效率和功率优化的角度对该模型展开分析。此外,我们使用不同的协议,并采用梯度下降算法对这些协议进行最佳拟合,以在有限循环时间下获得最优效率,进而获得最优功率。在效率优化过程中,所有协议均收敛于分段常数协议。之后,我们探索了一种更通用的方法,即利用变分原理确定用于优化功率和效率的最优协议。在功率和效率的优化过程中,净熵产降低,从而提升了热机的性能。该方法表明,与梯度下降算法相比,其能对该系统的效率和功率实现更优的优化效果。

英文摘要:

We study the behavior of a single spin in the presence of a time-varying magnetic field utilizing Glauber dynamics. We engineer the system to function as an engine by changing the magnetic field according to specific protocols. Subsequently, we analyze the engine's performance using various protocols and stochastic thermodynamics to compute average values of crucial quantities for quantifying engine performance. In the longtime limit of the engine cycle, we derive exact analytical expressions for work, heat, and efficiency in terms of a generalized protocol. We then analyze the model in terms of optimization of efficiency and power. Additionally, we use different protocols and employ a gradient descent algorithm to best fit those to obtain optimal efficiency and then optimal power for a finite cycle time. All the protocols converge to the piece-wise constant protocol during efficiency optimization. We then explore a more general approach using the variational principle to determine the optimal protocols for optimizing power and efficiency. During the optimization process for both power and efficiency, the net entropy production decreases, which enhances the engine's performance. This approach demonstrates the superior optimization of efficiency and power in this system compared to the gradient descent algorithm.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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