Freezeout at constant energy density and spin polarization in heavy-ion collisions

Using the local equilibrium density operator, we develop a geometry-informed linear response theory that takes into account the parameterization of the freezeout hypersurface before the gradient expansion is carried out. Assuming local equilibrium on an iso-energy density hypersurface, we study the $\Lambda$ hyperon spin polarization, and compute corrections to the isothermal case due to finite density. We argue that corrections to isothermal freezeout should be small, and that even in heavy ion collisions with energy as low as $\sqrt{s_{NN}}= 11.5$ GeV they constitute at most a $10\%$ effect. They may, however, become relevant for local polarization observables.