Global thermodynamics for isothermal fluids under gravity

TL;DR

This paper introduces a global thermodynamics framework for fluids under gravity, incorporating gravitational potential into free energy, and validates it with molecular dynamics simulations, revealing stable liquid-gas configurations and phase transitions.

Contribution

It extends thermodynamics to include gravity effects with a consistent potential reference, enabling analysis of equilibrium states and phase transitions in gravitational fields.

Findings

Liquid phase is stable at the bottom due to gravity.

Inverted liquid configuration is also locally stable.

First-order phase transition characterized by free energy landscape.

Abstract

We develop a formulation of global thermodynamics for equilibrium systems under the influence of gravity. The free energy for simple fluids is extended to include a dependence on $(T, V, N, mgL)$, where $L$ represents the vertical system length in the direction of gravity. A central idea in this formulation is to uniquely fix the reference point of the gravitational potential, ensuring a consistent thermodynamic framework. Using this framework, we derive the probability density of thermodynamic quantities, which allows us to define a variational function for determining equilibrium liquid-gas coexistence under gravity. The resulting free energy landscape, derived from the variational function, reveals the local stability of liquid-gas configurations. Specifically, the liquid phase resides at the lower portion of the system due to gravity, while the inverted configuration (with liquid on top) is also locally stable in this landscape. Furthermore, we characterize the transition between these liquid-gas configurations as a first-order phase transition using the thermodynamic free energy of $(T,V,N,mgL)$. Finally, we validate the predictions of global thermodynamics through molecular dynamics simulations, demonstrating the applicability and accuracy of the proposed framework.