Nonlinear analysis of causality for heat flow in heavy-ion collisions: Constraints from the equation of state

The present work investigates the causal parameter space of the Mueller-Israel-Stewart second-order theory for heat-conducting fluids in the Eckart frame for one-dimensional fluid flow in systems with finite baryon density. It is shown that this parameter space is highly constrained and particularly sensitive to the equation of state and second-order transport coefficients. Through numerical analysis of the characteristic equations, the present analysis identifies regions of strong hyperbolicity, weak hyperbolicity, and non-hyperbolicity, mapping the boundaries of causality violation as functions of the heat flux to energy density ratio $q/\varepsilon$ and relaxation parameters. The present work also explores the causality conditions using a realistic lattice QCD-based equation of state. Using the Navier-Stokes approximation, an estimate is made of the heat flow magnitude to assess causality criteria for one-dimensional heat conduction in heavy-ion collisions. The present calculations reveal unrealistically large heat flux values ($|{\bf{q}}|/\varepsilon \approx 330$--$811$) for typical RHIC conditions when using thermal conductivity estimates from kinetic theory models, suggesting either significant overestimation of transport coefficients or breakdown of the fluid approximation in these extreme conditions. The pressure gradient corrections reduce the heat flow by approximately 15\% but do not resolve the causality concerns.