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.

No abstract

We present a theoretical model to study the origin of chiral symmetry breaking of a racemic mixture of optically active biomolecules. We consider a collection of Brownian particles, which can stay in any of the three possible isomeric states: one achiral and two enantiomers. Isomers are undergoing self-regulatory reaction along with chiral inhibition and achiral decay processes. The reaction rates of the isomeric states are guided by their neighbors as well as the thermal fluctuations of the system. We find that an alteration in the relative dominance of self-regulation, chiral inhibition, and achiral decay processes breaks the chiral symmetry of the system, which is either partial or complete. This results in four different asymmetric population states, viz., three-isomer coexistence, enantiomeric coexistence, chiral–achiral coexistence, and homochiral state. A change in the reaction condition induces nonequilibrium transition among these states. We also report that a fast stochastic self-regulation and a slow chiral inhibition and achiral decay process along with a threshold population of interacting neighbors suffice for the requisite for transition toward a completely symmetry broken state, i.e., homochirality.

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.