Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant at both the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression or decompression situation.

中文翻译：

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有限时间绝热过程：导数和速度极限

获得在给定时间内连接平衡状态的绝热过程对于介观系统是一个挑战。在本文中，我们明确显示了如何在任意电位下为过阻尼的布朗粒子建立这些有限时间的绝热过程，该系统在概念和实践层面上都是相关的。这可以通过共同设计结合电位和流体温度的时间变化来实现。此外，我们证明了第二个原理对这种绝热转换施加了速度限制：出现了连接初始状态和最终状态的最短时间。可以为一般压缩或解压缩情况显式计算该最短时间。