# Consistent Implementation of Finite-Range Terms into Hydrodynamics

## TL;DR

This paper develops a formalism to incorporate finite-range interaction effects into hydrodynamics, modifying thermodynamic quantities and ensuring conservation laws, with applications to phase boundaries and correlation functions.

## Contribution

A new formalism for including finite-range gradient terms into hydrodynamics that preserves conservation laws and modifies thermodynamic expressions.

## Key findings

- Derived static solutions with zero temperature, chemical potential, and acceleration.
- Calculated phase boundary and correlation function profiles with gradient modifications.
- Introduced an additional noise term for accurate density-density correlation generation.

## Abstract

Non-zero-range interactions are often incorporated into mean field theories through gradient terms. Here, a formalism is developed to incorporate such terms into hydrodynamics. These terms alter expressions for the entropy, chemical potential, temperature and the stress-energy tensor. The formalism respects local conservation of energy, charge and entropy. The formalism leads to static solutions where the temperature, chemical potential and hydrodynamic acceleration all vanish, even when the density profile might be non-uniform. Profiles for a phase boundary and for correlation functions are calculated to illustrate the gradient modifications for various thermodynamic quantities. Also, for hydrodynamic calculations that add thermal noise to generate density-density correlations of the desired strength, an additional noise term is derived so that, at equilibrium, correlations are generated with both the correct size and length scale.