  The exclusive presence of $\beta$-D-ribofuranose in nucleic acids is still a
conundrum in prebiotic chemistry, given that pyranose species are substantially
more stable at equilibrium. However, a precise characterisation of the relative
furanose/pyranose fraction at temperatures higher than about 50$^{\,\rm o}$C is
still lacking. Here, we employ a combination of NMR measurements and
statistical mechanics modelling to predict a population inversion between
furanose and pyranose at equilibrium at high temperatures. More importantly, we
show that a steady temperature gradient may steer an open isomerisation network
into a non-equilibrium steady state where furanose is boosted beyond the limits
set by equilibrium thermodynamics. Moreover, we demonstrate that nonequilibrium
selection of furanose is maximum at optimal dissipation, as gauged by the
temperature gradient and energy barriers for isomerisation. The predicted
optimum is compatible with temperature drops found in hydrothermal vents
associated with extremely fresh lava flows on the seafloor.
