Causal and stable stochastic relativistic hydrodynamics

Heavy-ion collisions lead to the creation of one of the most exotic known types of fluids, the quark-gluon plasma. Due to the small size of the created system and the expected presence of a critical point in the transition from ordinary hadronic matter to the quark-gluon plasma, thermal fluctuations should be important in the modeling of this matter. In this dissertation, we focus on causal and stable formulations of stochastic relativistic hydrodynamics. Connections between causality, stability, and the foliation independence of equal-time fluctuations are used to formulate stochastic hydrodynamics in the linear regime. This approach is applied to several conventional theories of relativistic hydrodynamics, finding that new subtleties appear when fluctuations are included. To extend these results to the nonlinear regime, we consider effective action approaches. The standard procedures can lead to a non-convergent path integral and non-positive definite noise, so we introduce a new effective theory based on Crooks fluctuation theorem. This effective theory is applied to divergence-type hydrodynamics, in which case the path integral can converge and both causality and stability conditions can be enforced with relative ease. This formulation leads to equations that are flux conservative and so can be simulated using the Metropolis algorithm, supporting the inclusion of stochastic fluctuations in the modeling of heavy-ion collisions.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Mullins, Nicki

Contributors dc:contributor

• Noronha, Jorge
• Noronha-Hostler, Jacquelyn
• Sickles, Anne
• Witek, Helvi

• stochastic dynamics
• relativistic hydrodynamics
• quark-gluon plasma
• heavy-ion collisions
• high-energy nuclear theory

Statement dc:rights

• Copyright 2025 Nicki Mullins

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132475

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132475