发表机构
Eötvös Loránd University; Wigner Research Centre for Physics; Budapest University of Technology and Economics（厄特沃什·罗兰大学; 维格纳物理研究中心; 布达佩斯技术与经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于热力学第二定律推导无Ostrogradsky不稳定性的高阶梯度牛顿引力，得到牛顿力定律及无耗散交叉耦合，通过正则性约束Yukawa型修正，平方反比定律测试限制了最大内部长度。
AI 中文摘要
高阶梯度修正的牛顿引力可消除点质量奇点，但其拉格朗日动力学受Ostrogradsky不稳定性困扰。本文证明，将热力学第二定律应用于具有弱非局域态空间的自引力流体，可得到相同的场方程，且该路径下天生无此不稳定性：势满足一阶弛豫方程，即梯度流，其李雅普诺夫函数为熵密度，且仅当熵为凹函数时，弛豫谱在所有波数下均为负定。该推导还得到了压强张量和能量流，一个精确恒等式无需额外输入即可重现牛顿力定律，还得到了与体粘滞压强的无耗散交叉耦合，这是变分原理无法产生的。正则性通过振幅求和规则约束 Yukawa型修正，即∑ᵢαᵢ=-1，因此平方反比定律的实验室测试将最大内部长度限制在4×10⁻⁵米以下，并将复根区确定为经典一致的Lee–Wick类部分。
英文摘要
Higher-gradient modifications of Newtonian gravity remove the point-mass singularity, but their Lagrangian dynamics is haunted by the Ostrogradsky instability. We show that the same field equations follow from the Second Law of thermodynamics applied to a self-gravitating fluid with a weakly nonlocal state space, and that on this route the instability is absent by construction: the potential obeys a first-order relaxation equation that is a gradient flow, whose Lyapunov function is the entropy density, and whose relaxation spectrum is negative definite at every wavenumber precisely when the entropy is concave. The derivation also yields the pressure tensor and the energy current, an exact identity that reproduces Newton's force law without further input, and a dissipation-free cross-coupling to the bulk viscous pressure that no variational principle can produce. Regularity constrains the Yukawa-type corrections by an amplitude sum rule, $\sum_iα_i=-1$, so that laboratory tests of the inverse-square law bound the largest internal length below $4\times10^{-5}$~m, and identify the complex-root regime as a classically consistent Lee--Wick-like sector.
Comments4 pages, no figures
