Li Geng, Tu Z C
CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Graduate School of China Academy of Engineering Physics, Beijing 100193, China.
Phys Rev E. 2021 Mar;103(3-1):032146. doi: 10.1103/PhysRevE.103.032146.
Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties of physical, chemical, and biological systems. The discovery of the Jarzynski equality illumines the way to estimate the equilibrium free-energy difference from the work performed in nonequilibrium driving processes. However, the nonlinear (exponential) relation causes the poor convergence of the Jarzynski equality. Here, we propose a concise method to estimate the free-energy difference through a linear nonequilibrium equality which inherently converges faster than nonlinear nonequilibrium equalities. This linear nonequilibrium equality relies on an accelerated isothermal process which is realized by using a unified variational approach, named variational shortcuts to isothermality. We apply our method to an underdamped Brownian particle moving in a double-well potential. The simulations confirm that the method can be used to accurately estimate the free-energy difference with high efficiency. Especially during fast driving processes with high dissipation, the method can improve the accuracy by more than an order of magnitude compared with the estimator based on the nonlinear nonequilibrium equality.
从非平衡测量中提取平衡信息是理解物理、化学和生物系统热力学性质的一项极具重要性的挑战性任务。雅尔津斯基等式的发现为从非平衡驱动过程中执行的功来估计平衡自由能差指明了道路。然而，非线性（指数）关系导致雅尔津斯基等式收敛性较差。在此，我们提出一种简洁方法，通过一个线性非平衡等式来估计自由能差，该等式本质上比非线性非平衡等式收敛得更快。这个线性非平衡等式依赖于一个加速等温过程，该过程通过使用一种统一的变分方法来实现，即等温变分捷径。我们将我们的方法应用于在双阱势中运动的欠阻尼布朗粒子。模拟结果证实，该方法可用于高效准确地估计自由能差。特别是在具有高耗散的快速驱动过程中，与基于非线性非平衡等式的估计器相比，该方法能将精度提高一个多数量级。
