DOI: 10.1063/5.0350993 ISSN: 1070-6631

Density evolution in inhomogeneous fluids from a kinetic Gibbs–Duhem relation

Fei Wang
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The classical Gibbs–Duhem relation is restricted to quasistatic thermodynamic processes and does not include kinetic energy contributions. Consequently, its connection to fluid mechanics remains indirect. Here, we derive a kinetic Gibbs–Duhem relation that consistently incorporates kinetic effects, thereby linking thermodynamic and mechanical descriptions of fluid motion. On this basis, we formulate a density evolution equation for inhomogeneous fluids. The proposed equation recovers, as limiting cases, the classical relations for the speed of sound, Bernoulli's equation, and the van der Waals equation of state.

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