Fig. 5.

Monte Carlo sampling for maximally informative currents. We seek a weighting vector field d such that the TUR bound is as close to the true entropy production rate as possible. Starting either with d = F (blue curve) or with a random vector field (red curve), a Markov chain Monte Carlo procedure was used to change d in search of a higher ${\dot{S}}_{\mathrm{TUR}}^{\left(\mathbf{d}\right)}∕{\dot{S}}_{\mathrm{ss}}$ ratio. The Monte Carlo sampling discovers diverse ways to yield a similar maximal value of the TUR ratio, suggesting that while the optimization problem is not dominated by a single basin, competitive near-optimal solutions can be discovered from a variety of starting points