AI 中文总结
本文针对已解波动率随机流体公式开发变密度热力学扩展，结合有限关联储层等得到熵可容性结果，零波动率极限下恢复经典可压缩Navier-Stokes-Fourier方程，经典型计算验证相关性质。
AI 中文摘要
本文针对arXiv:2607.25536的已解波动率随机流体公式，开发了变密度热力学扩展形式。含源随机输运将质量、动量和总能量守恒分解为时间演化偏微分方程与鞅相容性约束。密度和温度为原始热力学场：质量守恒决定密度，内能决定温度，状态方程沿随机粒子路径确定压力演化。已解动能恒等式与有限关联储层、Green-Kubo校准、平衡抵消项及已解-未解伴随交换相结合。随机Gibbs恒等式和高斯相对熵为Hencky储层公式产生条件熵可容性结果。区分状态方程压力波动与机械应力冲量：常规有限马赫数波动不产生独立白噪声体积压力冲量，而快速机械压力由因果有限关联载体表示。给出保守边界条件与量热完善理想气体特例。零波动率极限下，恢复经典可压缩Navier-Stokes-Fourier方程。冻结描述符分析识别出混合双曲-抛物漂移子系统，耦合代数鞅约束，含依赖闭合的椭圆块与奇异低马赫数压力极限。典型计算验证了压力载体、声学色散、粘热能平衡及低马赫数缩放。本文未声称非线性适定性、激波可容性及充分发展湍流。
英文摘要
A variable-density thermodynamic extension is developed for the solved-volatility stochastic-fluid formulation of arXiv:2607.25536. Source-inclusive stochastic transport separates mass, momentum and total-energy conservation into time-evolution partial differential equations and martingale compatibility constraints. Density and temperature are the primitive thermodynamic fields: mass conservation determines density, internal energy determines temperature, and the equation of state determines pressure evolution along stochastic particle paths. The resolved kinetic-energy identity is combined with a finite-correlation reservoir, Green--Kubo calibration, an equilibrium counterterm and adjoint resolved-unresolved exchange. A stochastic Gibbs identity and Gaussian relative entropy yield a conditional entropy-admissibility result for a Hencky-reservoir formulation. Equation-of-state pressure fluctuations are distinguished from mechanical stress impulses; regular finite-Mach fluctuations produce no independent white-noise bulk pressure impulse, while fast mechanical pressure is represented by a causal finite-correlation carrier. Conservative boundary conditions and a calorically perfect ideal-gas specialization are given. In the zero-volatility limit, the classical compressible Navier--Stokes--Fourier equations are recovered. A frozen descriptor analysis identifies a mixed hyperbolic--parabolic drift subsystem coupled to algebraic martingale constraints, with closure-dependent elliptic blocks and a singular low-Mach pressure limit. Canonical calculations verify the pressure carrier, acoustic dispersion, viscous-thermal energy balance and low-Mach scaling. Nonlinear well-posedness, shock admissibility and developed turbulence are not claimed.
Comments29 pages, 4 figures
