Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium
Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium
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DOI：
10.1103/physreve.106.044122
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发表时间：
2022-10-14
影响因子：
2.4
通讯作者：
Wang, Haina
中科院分区：
文献类型：
--
作者：
Torquato, Salvatore;Wang, Haina
在d维欧氏空间Rd中确定精确地产生正温度T下具有预定的对关联函数g2（r）或相应的结构因子S（k）的平衡态的对势v（r）是一个具有深远意义的杰出的逆统计力学问题。最近，Zhang和Torquato [Phys.Rev.E101，032124（2020）]指出，任何对应于一个几何不变的非平衡系统的可实现的g2（r）或S（k）都可以通过一个只涉及（至多）有效对相互作用的经典平衡系综来获得。测试这个猜想的非平衡系统以及非平凡的平衡状态，需要改进的逆方法。我们已经设计了一个优化算法，以精确地确定有效的对电位，对应于对统计的一般conventionally不变的无序多体平衡或非平衡系统在正温度下。这种方法利用了一个参数化的家庭逐点基函数的潜在功能，其初始形式是由小，中，大距离的行为，由统计力学理论。随后，利用非线性优化技术来最小化目标函数，该目标函数结合了目标对相关函数g2（r）和结构因子S（k），使得非常准确地捕获小的中间距离和大距离相关。为了说明我们的方法的通用性和力量，我们准确地确定了以下四个不同的目标系统的有效对相互作用：（1）Lennard-Jones系统在其临界点附近，（2）液体下的Dzugutov势，（3）非平衡随机顺序添加包装，和（4）非平衡超均匀的“隐形”均匀随机晶格。我们发现，优化的对电位产生相应的对统计，准确地匹配其相应的目标与总L2范数误差是一个数量级小于以前的方法。我们的研究结果进一步支持了Zhang-Torquato猜想。此外，我们的算法将使一个探测系统具有相同的对统计，但不同的更高的身体统计，这将揭示著名的统计力学的简并问题。
The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g2(r) or corresponding structure factor S(k) in d-dimensional Euclidean space Rd is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)] conjectured that any realizable g2(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate-and large-distance behaviors dictated by statistical -mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g2(r) and structure factor S(k) so that the small intermediate-and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L2-norm errors that are an order of magnitude smaller than that of previous methods. The results of our investigation lend further support to the Zhang-Torquato conjecture. Furthermore, our algorithm will enable one to probe systems with identical pair statistics but different higher-body statistics, which will shed light on the well-known degeneracy problem of statistical mechanics.