A realization of a two-dimensional flow with a∗ = b∗ = c∗ = 1, κ∗ = 0.5, and N = 200 particles. (Left) The BP Bethe free energy as a function of the diffusivity κ and the shear b, where every point is obtained by minimizing with respect to the stretching a and the vorticity c of the flow. (Right) The same free energy in a contour plot, showing the maximum close to b = 1 and κ = 0.5. The maximum is achieved for , bBP = 1.026(1), cBP = 0.945(1), and κBP = 0.509(1), where the parentheses indicates numerical error on the third digit.