发表机构
Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将流体密度视为概率密度，通过熵演化揭示宏观可压缩性与微观扩散对熵产生的影响，并给出压缩混合层厚度标度律，经数值模拟验证，为不可逆性提供分析框架。
AI 中文摘要
连续性方程是连续介质中质量输运的基本原理。虽然其数学结构与概率输运和刘维尔方程相似，但在工程背景下，对宏观流体流动的信息论解释较少被探索。本文将流体密度视为空间概率密度函数，将宏观运动建模为不确定性的连续输运。我推导了在一般流动条件下香农熵的时间演化，确立了熵产生如何依赖于宏观可压缩性和微观扩散。微观扩散被证明是一个严格正的熵源，其大小精确地由局部费舍尔信息决定。此外，该框架导出了一个显式的代数标度律，表征了在局部佩克莱数为1时压缩混合层的平衡厚度。该理论模型通过一维典型流动和三维空间变化阿诺尔德-贝尔特拉米-柴尔德里斯（ABC）流中的对流-扩散方程的有限差分模拟进行了计算验证，平均相对误差为0.001。该框架为热力学不可逆性提供了分析视角，在湍流建模、热交换器中的热熵产生、内燃机缸内混合以及气动流动方面具有潜在应用。
英文摘要
The continuity equation serves as a fundamental principle for mass transport in continuous media. While its mathematical structure mirrors that of probability transport and the Liouville equation, an informational interpretation of macroscopic fluid flow is less commonly explored in engineering contexts. This paper treats fluid density as a spatial probability density function, modeling macroscopic motion as the continuous transport of uncertainty. I derive the temporal evolution of Shannon entropy under general flow conditions, establishing how entropy generation depends on macroscopic compressibility and microscopic diffusion. Microscopic diffusion is shown to act as a strictly positive entropy source governed exactly by local Fisher Information. Furthermore, the framework yields an explicit algebraic scaling law characterizing the equilibrium thickness of compressive mixing layers at a local Peclet number of unity. The theoretical model is computationally validated through finite-difference simulations of one-dimensional canonical flows and advection-diffusion within a three-dimensional, spatially varying Arnold-Beltrami-Childress (ABC) flow, yielding a mean relative error of $0.001$. The framework provides an analytical perspective on thermodynamic irreversibility, with potential applications to turbulence modeling, thermal entropy generation in heat exchangers, in-cylinder mixing in internal combustion engines, and aerodynamic flows.
CommentsPublished in Physica A: Statistical Mechanics and its Applications, Volume 699 (2026), Article 131908
Journal refA. Bhattacharjee, Fluid flow as transport of probability: Entropy, compressibility, and irreversibility, Physica A: Statistical Mechanics and its Applications 699 (2026) 131908
DOI：10.1016/j.physa.2026.131908
