Non-Gaussian fluctuation dynamics in relativistic fluids

Abstract

We consider non-equilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation time scales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.

arXiv comment29 pages, 8 figures. Version accepted by PRC

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• The QCD phase diagram and Beam Energy Scan physics: a theory overview
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• Simulations of stochastic fluid dynamics near a critical point in the phase diagram
• Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics
• System size and shape dependences of collective flow fluctuations in relativistic nuclear collisions