Speaker
Description
The observation of global polarization of $\Lambda$ hyperons in relativistic heavy-ion collisions has motivated the development of various theoretical frameworks to describe spin polarization in strongly interacting matter. One such framework is spin hydrodynamics, in which spin degrees of freedom are incorporated as hydrodynamic variables, thereby allowing the dynamics of angular momentum to be described within a hydrodynamic framework. In this description, each fluid element is assumed to carry both orbital and spin angular momentum, $\vec{J}=\vec{L}+\vec{S}$. Consequently, the hydrodynamic evolution of such a fluid must satisfy conservation of total angular momentum in addition to the conventional conservation laws.
In the present work, we study the evolution of spin hydrodynamic equations in a boost-invariant system, treating the spin chemical potential as a leading-order hydrodynamic variable. The constitutive equations are obtained using an entropy-current analysis, and we consider a minimal extension of the hydrodynamic theory up to second order in the gradient expansion, which ensures causal and stable evolution. Assuming a symmetric energy–momentum tensor and an independently conserved spin tensor, we obtain the coupled evolution equations of motion. Hydrodynamic noise is then introduced, following the fluctuation–dissipation theorem, to account for thermal fluctuations associated with the dissipative processes. A novel feature of this framework is the inclusion of spin dissipation and the corresponding spin transport coefficients and their fluctuations, which extend the conventional description of dissipative hydrodynamics. The hydrodynamic fluctuations are manifestations of thermal noise, which must be incorporated to achieve a consistent event-by-event description of the dynamical evolution of the system. We obtain the proper-time evolution of the thermodynamic variables and dissipative currents by solving the stochastic spin-hydrodynamic equations. We investigate the proper-time evolution of fluctuations in the dissipative spin currents along with those in the shear and bulk sectors of the energy–momentum tensor. This work establishes a novel, general framework for incorporating hydrodynamic fluctuations into spin hydrodynamics.
