Far-from-equilibrium search for the QCD critical point

Initial conditions for relativistic heavy-ion collisions may be far from equilibrium (i.e. there are large initial contributions from the shear stress tensor and bulk pressure) but it is expected that on very short time scales the dynamics converge to a universal attractor that defines hydrodynamic behavior. Thus far, studies of this nature have only considered an idealized situation at LHC energies (high temperatures $T$ and vanishing baryon chemical potential $\mu_B=0$) but, in this work, we investigate for the first time how far-from-equilibrium effects may influence experimentally driven searches for the Quantum Chromodynamic critical point at RHIC. We find that the path to the critical point is heavily influenced by far from equilibrium initial conditions where viscous effects lead to dramatically different $\left\{T,\mu_B\right\}$ trajectories through the QCD phase diagram. We compare hydrodynamic equations of motion with shear and bulk coupled together at finite $\mu_B$ for both DNMR and phenomenological Israel-Stewart equations of motion and discuss their influence on potential attractors at finite $\mu_B$ and their corresponding $\left\{T,\mu_B\right\}$ trajectories.