Thermodynamic uncertainty relations in mesoscopic devices.

We investigate the thermodynamic uncertainty relations (TURs) in mesoscopic devices for all universal symmetry classes of Wigner-Dyson and Dirac (chiral). The observables of interest include the TUR (MS), which is defined in terms of the ratio between the mean noise and mean conductance, as well as a new TUR (R) proposed in this article, which is based on the ensemble mean of the noise-to-conductance ratio. A detailed study is made on the quantum interference corrections associated with the TURs. We also analyze the influence of orbital and sublattice/chiral degrees of freedom for the validity of the observables in these chaotic mesoscopic billiards. Our investigation is based on the concatenation between the Landauer-Büttiker theory, the Mahaux-Wendeinmüller theory, and the TURs. We simulate the universal mesoscopic chaotic quantum dots using the random-matrix theory and compare our numerical results with the pertinent experimental data. The results were obtained for a different number of channels and tunneling rates that vary from the opaque to the ideal regime and, in all cases, demonstrate a clear phenomenological distinction between the TURs. In particular, the opaque regime engenders remarkable differences between the observables, even in the semiclassical regime, which characterizes a clear violation of the central limit theorem. Furthermore, we show that the phenomenology of the quantum interference corrections is strikingly robust, surprisingly exhibiting an order of magnitude greater than the supposedly leading semiclassical term for the TUR (R).

The Pht1;9 and Pht1;8 transporters mediate inorganic phosphate acquisition by the Arabidopsis thaliana root during phosphorus starvation.

• The activation of high-affinity root transport systems is the best-conserved strategy employed by plants to cope with low inorganic phosphate (Pi) availability, a role traditionally assigned to Pi transporters of the Pht1 family, whose respective contributions to Pi acquisition remain unclear. • To characterize the Arabidopsis thaliana Pht1;9 transporter, we combined heterologous functional expression in yeast with expression/subcellular localization studies and reverse genetics approaches in planta. Double Pht1;9/Pht1;8 silencing lines were also generated to gain insight into the role of the closest Pht1;9 homolog. • Pht1;9 encodes a functional plasma membrane-localized transporter that mediates high-affinity Pi/H⁺ symport activity in yeast and is highly induced in Pi-starved Arabidopsis roots. Null pht1;9 alleles exhibit exacerbated responses to prolonged Pi limitation and enhanced tolerance to arsenate exposure, whereas Pht1;9 overexpression induces the opposite phenotypes. Strikingly, Pht1;9/Pht1;8 silencing lines display more pronounced defects than the pht1;9 mutants. • Pi and arsenic plant content analyses confirmed a role of Pht1;9 in Pi acquisition during Pi starvation and arsenate uptake at the root-soil interface. Although not affecting plant internal Pi repartition, Pht1;9 activity influences the overall Arabidopsis Pi status. Finally, our results indicate that both the Pht1;9 and Pht1;8 transporters function in sustaining plant Pi supply on environmental Pi depletion.