Causal and stable stochastic relativistic hydrodynamics

Mullins, Nicki

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

Description

Title

Causal and stable stochastic relativistic hydrodynamics

Author(s)

Mullins, Nicki

Issue Date

2025-10-28

Director of Research (if dissertation) or Advisor (if thesis)

Noronha, Jorge

Doctoral Committee Chair(s)

Noronha-Hostler, Jacquelyn

Committee Member(s)

• Sickles, Anne
• Witek, Helvi

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2025-12

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2025 Nicki Mullins

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