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Description
In non-central heavy-ion collisions, the colliding nuclei carry a large amount of angular momentum, which can be transferred to the hot and dense partonic medium known as quark-gluon plasma (QGP) created in the interaction region. This gives rise to a vortical structure of the medium which is subsequently reflected in the polarization of final-state hadrons. Several theoretical frameworks have been developed to explain the spin polarization phenomenon of the detected hadrons. One such framework is spin hydrodynamics, in which spin degrees of freedom, or equivalently the total angular momentum, are incorporated as hydrodynamic variables. In this approach, each fluid element is assumed to possess both orbital and spin angular momentum $J=L+S$. Consequently, the hydrodynamic evolution of such a fluid must satisfy the conservation of total angular momentum in addition to the usual conservation laws. In the present work, we consider dissipative spin hydrodynamics up to second order. Such second order theories are expected to be consistent with linear stability and causality constraints. The novelty of spin hydrodynamic frameworks is the presence of spin dissipations and spin transport coefficients. These dissipations in energy momentum and spin tensor are accompanied by corresponding fluctuations in accordance with the fluctuation-dissipation theorem. Since coarse-graining results in the loss of information of microscopic degrees of freedom of the system, the hydrodynamic variables can fluctuate from event to event around their ensemble-averaged values. The fluctuations are manifestations of thermal noise and must be incorporated to achieve a consistent event-by-event description of the dynamical evolution of the system.
In this work, we investigate the hydrodynamic fluctuations associated with the second-order dissipative spin hydrodynamic theory. The spin chemical potential is treated as a leading order term in the gradient expansion and it affects the equation of state
We derive the spin hydrodynamic equations of motion for minimally extended second order spin hydrodynamics and also the Onsager coefficients associated with the noise correlators of the dissipative currents. We obtain the proper time evolution of conserved quantities and dissipative currents for a boost-invariant system using the Stratonovich algorithm. We show how fluctuations in the dissipative part of spin current evolve with proper time along with shear and bulk sector of the energy momentum tensor. This work establishes a general framework for incorporating hydrodynamic fluctuations into spin hydrodynamics