Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain.
Dipartimento di Fisica e Astronomia "Galileo Galilei", Istituto Nazionale di Fisica Nucleare, Università di Padova, Via Marzolo 8, 35131 Padova, Italy.
Phys Rev E. 2019 Jan;99(1-1):012140. doi: 10.1103/PhysRevE.99.012140.
We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness κ. We work out the optimal time dependence κ(t) by minimizing the work performed on the particle under the nonholonomic constraint 0≤κ≤κ_{max}, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analyzed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time t_{f} and the desired compression ratio κ_{f}/κ_{i}, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimization of heat engines.
我们应用庞特里亚金原理来快速驱动处于两个平衡态之间的被捕获的过阻尼布朗粒子，这两个平衡态对应于不同的阱硬度κ。我们通过最小化在非完整约束 0≤κ≤κ_{max} 下对粒子所做的功来得出最优的时间依赖性 κ(t)，这是一种与实验相关的情况。与文献中分析的无界硬度情况相比，会出现几个重要的差异。首先，两个任意的平衡态不一定总是连通的。其次，取决于操作时间 t_{f} 和所需的压缩比 κ_{f}/κ_{i}，会出现不同类型的解。最后，由边界引起的功的最小值的差异可能会变得非常大，这可能对热机的优化有重要影响。
