Consistent Implementation of Finite-Range Terms into Hydrodynamics

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.

Fixed typos in Eq.s, added references

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Cited by in corpus (5)

• Dynamical exploring the QCD matter at finite temperatures and densities-a short review
• Evolution of Charge Fluctuations and Correlations in the Hydrodynamic Stage of Heavy Ion Collisions
• Calculating n-Point Charge Correlations in Evolving Systems
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• Covariant formulation of spinodal decomposition in rapidly expanding quark gluon plasma