which is our input parameter. Our typical volume fractions ϕ ≈ 15% correspond to the reduced particle densities ρ ⋆ σ 3 ≈ 0.2 and box sizes L ≈ 30σ ≈ 7R g , where R g is the radius of gyration of a single chain. These volume fractions are still low enough to assure that the chains do not interact with their own periodic images through the boundary conditions. Upon reaching the final box size, we eventually re-tune the parameters of the PPPM method to the relative accuracy of 10 -3 and we equilibrate the system for 10 7 steps of Langevin dynamics (10 5 τ ) and 10 5 steps of Monte Carlo particle exchanges until time drifts in energies and pressures cease to be measurable.