Spin Hydrodynamics Enables Consistent Theory for Relativistic Fluids with Rank-3 Tensor Angular Momentum

Relativistic fluids, systems moving at speeds approaching the speed of light, often exhibit intrinsic angular momentum known as spin, a property increasingly recognised as crucial for understanding extreme states of matter. Asaad Daher, from the Henryk Niewodniczański Institute of Nuclear Physics Polish Academy of Sciences, along with colleagues, now presents a comprehensive theoretical framework for describing these spinning fluids, termed relativistic dissipative spin hydrodynamics. This work establishes a new set of equations that account for spin density, a measure of the fluid’s rotation, and its influence on the fluid’s behaviour, building upon established theories of fluid dynamics and statistical mechanics. The research addresses a growing need to explain recent observations of spin polarization in particles created during high-energy heavy-ion collisions, offering a pathway to interpret experimental results and refine our understanding of matter under extreme conditions, while also paving the way for further theoretical advances in the field.

The research addresses a growing need to explain recent observations of spin polarization in particles created during high-energy heavy-ion collisions, offering a pathway to interpret experimental results and refine our understanding of matter under extreme conditions, while also paving the way for further theoretical advances in the field.

The objective of this work is to develop a consistent theoretical framework for dissipative hydrodynamics of a relativistic spin fluid, referred to as relativistic dissipative spin hydrodynamics. Within this theory, a dynamic description of a relativistic fluid necessitates the introduction of spin density, which is associated with the spin tensor, contributing to the total angular momentum of the system. The need for such a theory arises from recent measurements of spin polarization of hadrons produced in non-central relativistic heavy-ion collisions.

The approach involves a two-pronged strategy, focusing on both theoretical development and comparison with experimental observations.

Foundations of Relativity, Physics and Group Theory

The research builds upon core theoretical foundations including relativity, statistical physics, and hydrodynamics, utilising group theory to understand symmetries relevant to spin and angular momentum. These foundational elements provide the necessary tools to bridge microscopic and macroscopic descriptions of physical systems, and connect thermodynamics with accelerated frames and non-equilibrium systems.

Spin Hydrodynamics and Relativistic Dissipation Theory

This work establishes a consistent theoretical framework for relativistic dissipative spin hydrodynamics, extending conventional theories to incorporate spin density as a crucial macroscopic variable. Recognizing that spin contributes to a system’s total angular momentum, the research addresses the need for a robust theory motivated by recent measurements of spin polarization observed in high-energy heavy-ion collisions.

Scientists developed two distinct yet complementary formulations, one based on covariant thermodynamics and the other on relativistic statistical mechanics, both designed to describe fluids with spin density as a fundamental variable. The resulting theories yield a system of equations governing the evolution of macroscopic variables and identify the associated dissipative currents and transport coefficients, offering new avenues for investigating spin polarization observed in high-energy collisions.

The team rigorously analyzed the stability of these equations, focusing on the rest-frame low-wavenumber limit and establishing constraints for the spin equation of state. Experiments involving systems subject to Bjorken flow revealed detailed insights into the evolution of temperature and spin potential, demonstrating predictable scaling with initial values. Measurements confirm that the magnitude of the spin potential, normalized to its initial value, also evolves predictably over time.

Further development of the theory involved a Müller-Israel-Stewart limit, exploring second-order dissipative currents and their associated transport coefficients. Linear mode analysis rigorously tested stability and causality, confirming the framework’s adherence to fundamental physical principles. A quantum-statistical formulation was also constructed, building upon principles of relativistic quantum mechanics to define local and global equilibrium conditions and derive an entropy current, enabling the identification of first-order dissipative currents and their irreducible decompositions under rotation.

The research delivers a powerful theoretical foundation for interpreting spin polarization measurements and opens avenues for future theoretical advancements and microscopic modeling.

Relativistic Spin Hydrodynamics, A Theoretical Framework

This work establishes a theoretical framework for relativistic dissipative spin hydrodynamics, extending established models to incorporate the influence of spin in fluid dynamics. Researchers developed two distinct yet complementary formulations, one based on covariant thermodynamics and the other on relativistic statistical mechanics, both designed to describe fluids with spin density as a fundamental variable.

The achievement lies in providing a consistent description of how spin affects the behavior of relativistic fluids, a crucial step towards more accurately modeling extreme conditions found in phenomena like heavy-ion collisions. Importantly, the study demonstrates that total angular momentum arises from both orbital and spin components, differing from systems without intrinsic spin. The authors acknowledge that further work is needed to verify the thermodynamic relations within their framework using microscopic approaches and to refine the understanding of transport coefficients through detailed modeling or experimental data, potentially applying these theories to specific physical systems and comparing predictions with ongoing experimental measurements of spin polarization.