Fluctuations in relativistic causal hydrodynamics

Formalism to calculate the hydrodynamic fluctuations by applying the Onsager theory to the relativistic Navier–Stokes equation is already known. In this work, we calculate hydrodynamic fluctuations within the framework of the second order hydrodynamics of Müller, Israel and Stewart and its generalization to the third order. We have also calculated the fluctuations for several other causal hydrodynamical equations. We show that the form for the Onsager-coefficients and form of the correlation functions remain the same as those obtained by the relativistic Navier–Stokes equation and do not depend on any specific model of hydrodynamics. Further we numerically investigate evolution of the correlation function using the one dimensional boost-invariant (Bjorken) flow. We compare the correlation functions obtained using the causal hydrodynamics with the correlation function for the relativistic Navier–Stokes equation. We find that the qualitative behavior of the correlation functions remains the same for all the models of the causal hydrodynamics.