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分子动力学模拟中Jarzynski和Crooks非平衡功定理的推广

Generalization of the Jarzynski and Crooks nonequilibrium work theorems in molecular dynamics simulations.

作者信息

Chelli Riccardo, Marsili Simone, Barducci Alessandro, Procacci Piero

机构信息

Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, Sesto Fiorentino, Italy.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 1):050101. doi: 10.1103/PhysRevE.75.050101. Epub 2007 May 7.

Abstract

The Jarzynski identity [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and the Crooks equation [G. E. Crooks, J. Stat. Phys. 90, 1481 (1998)] relate thermodynamic free energy differences to the work done on a system during a collection of nonequilibrium transformations. In the present Rapid Communication we provide generalized versions of these nonequilibrium work theorems, which hold for dissipative transformations where the system may undergo simultaneously mechanical work and pressure-temperature or volume-temperature changes. The proof is valid in the context of dynamic systems that evolve with NPT -based equations of motion according to the Martyna-Tobias-Klein algorithm [Martyna J. Chem. Phys. 101, 4177 (1994)]. An extension of the proof to dynamic systems that evolve through NVT -based equations of motion is also provided. The theorems may be effectively used in non-Hamiltonian molecular dynamics simulations for evaluating Helmholtz or Gibbs free energy differences, or the ratio of partition functions at different temperatures to be eventually used in thermodynamic cycles.

摘要

雅津斯基恒等式[C. 雅津斯基,《物理评论快报》78, 2690 (1997)]和克鲁克斯方程[G. E. 克鲁克斯,《统计物理杂志》90, 1481 (1998)]将热力学自由能差与在一系列非平衡变换过程中对系统所做的功联系起来。在本快报中,我们给出了这些非平衡功定理的广义形式,它们适用于耗散变换,在此过程中系统可能同时经历机械功以及压力 - 温度或体积 - 温度变化。证明在基于NPT运动方程并根据马尔蒂纳 - 托拜厄斯 - 克莱因算法[马尔蒂纳,《化学物理杂志》101, 4177 (1994)]演化的动力学系统的背景下是有效的。还给出了将证明扩展到基于NVT运动方程演化的动力学系统的情况。这些定理可有效地用于非哈密顿分子动力学模拟,以评估亥姆霍兹或吉布斯自由能差,或不同温度下配分函数的比值,最终用于热力学循环。

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