发表机构
Mapúa University; Eastern Mediterranean University（马普阿大学; 东地中海大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出 Maxwell-Jüttner 平均的相对论非仿射剪切黏度理论，用平衡动量平均替代单一洛伦兹因子增强，分离运动学与动力学效应，并推导非相对论与极端相对论极限及高温定律条件。
AI 中文摘要
我们为经典有质量粒子气体构建了相对论非仿射剪切黏度理论的 Maxwell-Jüttner 平均扩展。出发点是基于广义朗之万动力学推导的相对论非仿射响应公式，其中固有动量耗散产生洛伦兹因子对黏度的增强。由于热相对论气体并非由单一洛伦兹因子表征，我们将此标量增强替换为对 Maxwell-Jüttner 分布的平衡动量平均。在本工作采用的标量横向平均场闭合内，最小相对论修正为洛伦兹因子的 Maxwell-Jüttner 平均，并成为 $\zeta=mc^2/(k_BT)$ 的有限质量增强函数。在一般闭合中，被平均的对象是洛伦兹因子、零频记忆核与非仿射仿射力关联函数的完整乘积。这一构造将运动学相对论增强与体现在浴记忆和集体模谱中的动力学耗散分离开来。我们推导了非相对论和极端相对论极限，表明一种特定的有效硬球标度能重现经典平方根定律作为一致性检验，并识别了三次方高温定律成立的条件。与相对论动力学理论实例的比较阐明，除非指定微观闭合，记忆核并不等同于弛豫时间。保留完整频率依赖则产生弛豫谱。单个主导极点将此谱约化为一个剪切弛豫时间，并给出通常的瞬态剪切方程。
英文摘要
We formulate a Maxwell-Jüttner averaged extension of relativistic nonaffine shear-viscosity theory for a classical gas of massive particles. The starting point is the relativistic nonaffine response formula derived from generalized Langevin dynamics, where proper-momentum dissipation produces a Lorentz-factor enhancement of the viscosity. Since a thermal relativistic gas is not characterized by a single Lorentz factor, we replace this scalar enhancement by an equilibrium momentum average over the Maxwell-Jüttner distribution. Within the scalar transverse mean-field closure used in this work, the minimal relativistic correction is the Maxwell-Jüttner mean of the Lorentz factor and becomes a finite-mass enhancement function of $ζ=mc^2/(k_BT)$. In the general closure, the averaged object is the full product of the Lorentz factor, the zero-frequency memory kernel, and the nonaffine affine-force correlator. This construction separates kinematic relativistic enhancement from dynamical dissipation encoded in the bath memory and collective mode spectrum. We derive the nonrelativistic and ultrarelativistic limits, show that a specified effective hard-sphere scaling reproduces the classical square-root law as a consistency test, and identify the assumptions under which a cubic high-temperature law follows. Comparison with relativistic kinetic-theory examples clarifies that the memory kernel is not equivalent to a relaxation time unless a microscopic closure is specified. Retaining the full frequency dependence instead yields a relaxation spectrum. A single dominant pole reduces this spectrum to one shear relaxation time and gives the usual transient shear equation.
Comments26 pages, 8 figures. Under review in Physical Review E. Comments are welcome
