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首页> 外文期刊>The Journal of Chemical Physics >Diffusion Monte Carlo study on temporal evolution of entropy and free energy in nonequilibrium processes
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Diffusion Monte Carlo study on temporal evolution of entropy and free energy in nonequilibrium processes

机译：蒙特卡罗扩散研究非平衡过程中熵和自由能的时间演化

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A computational scheme to describe the temporal evolution of thermodynamic functions in stochastic nonequilibrium processes of isothermal classical systems is proposed on the basis of overdamped Langevin equation under given potential and temperature. In this scheme the associated Fokker-Planck-Smoluchowski equation for the probability density function is transformed into the imaginary-time Schrodinger equation with an effective Hamiltonian. The propagator for the time-dependent wave function is expressed in the framework of the path integral formalism, which can thus represent the dynamical behaviors of nonequilibrium molecular systems such as those conformational changes observed in protein folding and ligand docking. The present study then employs the diffusion Monte Carlo method to efficiently simulate the relaxation dynamics of wave function in terms of random walker distribution, which in the long-time limit reduces to the ground-state eigenfunction corresponding to the equilibrium Boltzmann distribution. Utilizing this classical-quantum correspondence, we can describe the relaxation processes of thermodynamic functions as an approach to the equilibrium state with the lowest free energy. Performing illustrative calculations for some prototypical model potentials, the temporal evolutions of enthalpy, entropy, and free energy of the classical systems are explicitly demonstrated. When the walkers initially start from a localized configuration in one- or two-dimensional harmonic or double well potential, the increase of entropy usually dominates the relaxation dynamics toward the equilibrium state. However, when they start from a broadened initial distribution or go into a steep valley of potential, the dynamics are driven by the decrease of enthalpy, thus causing the decrease of entropy associated with the spatial localization. In the cases of one- and two-dimensional asymmetric double well potentials with two minimal points and an energy barrier between them, we observe a nonequilibrium behavior that the system entropy first increases with the broadening of the initially localized walker distribution and then it begins to decrease along with the trapping at the global minimum of the potential, thus leading to the minimization of the free energy. (C) 2016 AIP Publishing LLC.
机译：在给定的电势和温度下，基于过阻尼的Langevin方程，提出了一种描述等温经典系统随机非平衡过程中热力学函数的时间演化的计算方案。在该方案中，将用于概率密度函数的相关Fokker-Planck-Smoluchowski方程转换为具有有效哈密顿量的虚时Schrodinger方程。随时间变化的波函数的传播子在路径积分形式学的框架中表示，因此可以表示非平衡分子系统的动力学行为，例如在蛋白质折叠和配体对接中观察到的构象变化。然后，本研究采用扩散蒙特卡罗方法，根据随机沃克分布有效地模拟了波函数的松弛动力学，该函数在长期范围内会降低为与平衡玻尔兹曼分布相对应的基态本征函数。利用这种经典的量子对应关系，我们可以将热力学函数的弛豫过程描述为一种具有最低自由能的平衡态的方法。通过对一些原型模型势进行说明性计算，可以清楚地证明经典系统的焓，熵和自由能的时间演化。当步行者最初从一维或二维谐波或双阱势的局部配置开始时，熵的增加通常主导着趋向平衡态的弛豫动力学。但是，当它们从扩大的初始分布开始或进入陡峭的电势谷时，动力学受焓的减少驱动，从而导致与空间定位相关的熵的减少。在具有两个最小点和它们之间的能垒的一维和二维非对称双阱势的情况下，我们观察到一种非平衡行为，系统熵首先随着初始局部沃克分布的扩大而增加，然后开始随势阱全局最小值的捕获而减小，从而导致自由能最小化。 （C）2016 AIP出版有限责任公司。

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