We design a geometric Brownian information engine by considering overdamped Brownian particles inside a two-dimensional monolobal confinement with irregular width along the transport direction. Under such detention, particles experience an effective entropic potential which has a logarithmic form. We employ a feedback control protocol as an outcome of error-free position measurement. The protocol comprises three stages: measurement, feedback, and relaxation. We reposition the center of the confinement to the measurement distance (xp) instantaneously when the position of the trapped particle crosses xp for the first time. Then, the particle is allowed for thermal relaxation. We calculate the extractable work, total information, and unavailable information associated with the feedback control using this equilibrium probability distribution function. We find the exact analytical value of the upper bound of extractable work as (53−2ln2)kBT. We introduce a constant force G downward to the transverse coordinate (y). A change in G alters the effective potential of the system and tunes the relative dominance of entropic and energetic contributions in it. The upper bound of the achievable work shows a crossover from (53−2ln2)kBT to 12kBT when the system changes from an entropy-dominated regime to an energy-dominated one. Compared to an energetic analog, the loss of information during the relaxation process is higher in the entropy-dominated region, which accredits the less value in achievable work. Theoretical predictions are in good agreement with the Langevin dynamics simulation studies.

Dimethylglyoxime (DMG) usually forms thermodynamically stable chelating complexes with selective divalent transitionmetal ions. Electronic and spectral properties of metal-DMG complexes are highly dependent on the nature of metal ions. Using range-separated hybrid functional augmented with dispersion corrections within density functional theory (DFT) and time-dependent DFT, we present a detailed and comprehensive study on structural, electronic, and spectral (both IR and UV−vis) properties of M(DMG) 2 [M = Ni 2+ , Cu 2+ ] complexes. Ni(DMG) 2 results are thoroughly compared with Cu(DMG) 2 and also against available experimental data. Stronger H-bonding leads to greater stability of Ni(DMG) 2 with respect to isolated ions (M 2+ and DMG − ) compared to Cu(DMG) 2 . In contrast, a relatively larger reaction enthalpy for Cu(DMG) 2 formation from chemically relevant species is found than that of Ni(DMG) 2 because of the greater binding enthalpy of [Ni(H 2 O) 6 ] 2+ than that of [Cu(H 2 O) 6 ] 2+ . In dimers, Ni(DMG) 2 is found to be 6 kcal mol −1 more stable than Cu(DMG) 2 due to a greater extent of dispersive interactions. Interestingly, a modest ferromagnetic coupling (588 cm −1 ) is predicted between two spin-1 / 2 Cu 2+ ions present in the Cu(DMG) 2 dimer. Additionally, the potential energy curves calculated along the O−H bond coordinate for both complexes suggest asymmetry and symmetry in the H-bonding interactions between the H-bond donor and acceptor O centers in the solid-state and in solution, respectively, well corroborating with early experimental findings. Interestingly, a lower proton transfer barrier is obtained for the Ni(DMG) 2 compared to its Cu-analogue due to stronger H-bonding in the former complex. In fact, relatively weaker H-bonding in Cu(DMG) 2 results in blue-shifted O−H stretching modes compared to that in Ni(DMG) 2 . On the other hand, qualitatively similar optical absorption spectra are obtained for both complexes with red-shifted peaks found for the Cu(DMG) 2 . Finally, computational models for axial monoand diligand (aqua and ammonia) coordinated M(DMG) 2 complexes are predicted to be energetically feasible and stable with relatively greater binding stability obtained for the ammonia-coordination.

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The continuous heating of the Earth's surface and aerosphere causes global warming. Recent developments predict that at the end of the twenty-first century, with 3$^\circ$C on average global warming will yield a regional augmentation in the probability of the abnormally large precipitation accumulation in a single downpour event. We examine this issue using a stochastic climate model and provide a theoretical scheme to the increased possibility of cloudburst in a single rainfall event. We find that implementing a permanent upper cut-off in column integrated water vapour or an asymmetric stochastic resetting can reduce the abnormally high accumulation probability of such rainstorms. We report that an optimum upper limit of column integrated water vapour in the atmosphere ascertain the decrease in the heavy precipitation-accumulation. The presence of such a perpetual upper ceiling in the moisture content is energy exorbitant and can significantly affect the mean downpour. A careful choice of the system parameters ensures the decrease in mean accumulation size within a ten per cent tolerance limit. We introduce an asymmetric stochastic resetting to the amount of column integrated water vapour at its upper threshold to recompense the energy cost. We perceive that an adaptive restart rate is efficient enough to reduce the probability of targeted precipitation accumulation to the desired extent.

We investigate a Geometric Brownian Information Engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into extractable work. Outcomes of the information engine depend on the reference measurement distance x m , feedback site x f and the transverse force G. We determine the benchmarks for utilizing the available information in an output work and the optimum operating requisites for best work extraction. Transverse bias force (G) tunes the entropic contribution in the effective potential and hence the standard deviation (σ ) of the equilibrium marginal probability distribution. We recognize that the amount of extracted work reaches a global maximum when x f = 2x m with x m ∼ 0.6σ , irrespective of the extent of the entropic limitation. Because of the higher loss of information during the relaxation process, the best achievable work of a GBIE is lower in an entropic system. The feedback regulation also bears the unidirectional passage of particles. The average displacement increases with growing entropic control and is maximum when x m ∼ 0.81σ . Finally, we explore the efficacy of the information engine, a quantity that regulates the efficiency in utilizing the information acquired. With x f = 2x m , the maximum efficacy reduces with increasing entropic control and shows a cross over from 2 to 11/9. We discover that the condition for the best efficacy depends only on the confinement length scale along the feedback direction. The broader marginal probability distribution accredits the increased average displacement in a cycle and the lower efficacy in an entropy-dominated system.