Why hyperdensity functionals describe any equilibrium observable.

IF 2.3 4区 物理与天体物理 Q3 PHYSICS, CONDENSED MATTER Journal of Physics: Condensed Matter Pub Date : 2024-12-12 DOI:10.1088/1361-648X/ad98da
Florian Sammüller, Matthias Schmidt
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Abstract

We give an introductory account of the recent hyperdensity functional theory for the equilibrium statistical mechanics of soft matter systems (Sammülleret al2024Phys. Rev. Lett.133098201). Hyperdensity functionals give access to the behaviour of arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. The approach is based on classical density functional theory applied to an extended ensemble using standard functional techniques. The associated formally exact generalized Mermin-Evans functional relationships can be represented accurately by neural functionals. These neural networks are trained via simulation-based supervised machine learning and they allow one to carry out efficient functional calculus using automatic differentiation and numerical functional line integration. Exact sum rules, including hard wall contact theorems and hyperfluctuation Ornstein-Zernike equations, interrelate the different correlation functions. We lay out close connections to hyperforce correlation sum rules (Robitschkoet al2024Commun. Phys.7103) that arise from statistical mechanical gauge invariance (Mülleret al2024Phys. Rev. Lett.133217101). Further quantitative measures of collective self-organization are provided by hyperdirect correlation functionals and spatially resolved hyperfluctuation profiles. The theory facilitates to gain deep insight into the inherent structuring mechanisms that govern the behaviour of both simple and complex order parameters in coupled many-body systems.

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为什么高密度泛函描述任何可观察到的平衡。
本文介绍了软物质系统平衡统计力学的高密度泛函理论[F]。samm ller等人,物理学。[j].生物工程学报,2014,(5):481 - 481。高密度泛函给出了在空间非均匀平衡多体系统中任意热可观测值的行为。该方法以经典密度泛函理论为基础,利用标准泛函技术将其应用于扩展系综。相关的形式精确广义Mermin-Evans泛函关系可以用神经泛函有效地表示。这些神经网络通过基于模拟的监督机器学习进行训练,它们允许人们使用自动微分和数值函数线积分进行有效的函数演算。精确和规则,包括硬壁接触定理和超波动Ornstein-Zernike方程,使不同的相关函数相互关联。我们列出了与超强相关和规则的密切联系[S]。Robitschko等人,common。[J] .地球物理学报,2004,18(2):444 - 444。m勒等人,物理学。启。(出现);arXiv: 2406.19235)。集体自组织的进一步定量测量由超直接相关函数和空间分辨的超波动剖面提供。该理论有助于深入了解耦合多体系统中控制简单和复杂阶参量行为的内在结构机制。
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来源期刊
Journal of Physics: Condensed Matter
Journal of Physics: Condensed Matter 物理-物理:凝聚态物理
CiteScore
5.30
自引率
7.40%
发文量
1288
审稿时长
2.1 months
期刊介绍: Journal of Physics: Condensed Matter covers the whole of condensed matter physics including soft condensed matter and nanostructures. Papers may report experimental, theoretical and simulation studies. Note that papers must contain fundamental condensed matter science: papers reporting methods of materials preparation or properties of materials without novel condensed matter content will not be accepted.
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