Extracting work from a single heat bath: a case study of a Brownian particle under an external magnetic field in the presence of information

Achievable Information-Energy Exchange in a Brownian Information Engine through Potential Profiling

The information engine extracts work from a single heat bath using mutual information obtained during the operation cycle. This study investigates the influence of potential shaping in a Brownian information engine (BIE) in harnessing the information from thermal fluctuations. We designed a BIE by considering an overdamped Brownian particle inside a confined potential and introducing an appropriate symmetric feedback cycle. We find that the upper bound of the extractable work for a BIE with a monostable centrosymmetric confining potential, with a stable state at the potential center, depends on the bath temperature and the convexity of the confinement. A concave confinement is more efficient than a convex one for an information-energy exchange. For a bistable confinement with an unstable center and two symmetric stable basins, one can find an engine-to-refrigeration transition beyond a certain barrier height related to the energy difference between the energy barrier and the stable basins. Finally, we use the concavity-induced gain in information harnessing to device a BIE in the presence of a multistable potential that can harvest even more energy than monostable confinement.

Active Brownian information engine: Self-propulsion induced colossal performance

The information engine is a feedback mechanism that extorts work from a single heat bath using the mutual information earned during the measurement. We consider an overdamped active Ornstein-Uhlenbeck particle trapped in a 1D harmonic oscillator. The particle experiences fluctuations from an inherent thermal bath with a diffusion coefficient (D) and an active reservoir, with characteristic correlation time (τa) and strength (Da). We design a feedback-driven active Brownian information engine (ABIE) and analyze its best performance criteria. The optimal functioning criteria, the information gained during measurement, and the excess output work are reliant on the dispersion of the steady-state distribution of the particle's position. The extent of enhanced performance of such ABIE depends on the relative values of two underlying time scales of the process, namely, thermal relaxation time (τr) and the characteristic correlation time (τa). In the limit of τa/τr → 0, one can achieve the upper bound on colossal work extraction as ∼0.202γ(D+Da) (γ is the friction coefficient). The excess amount of extracted work reduces and converges to its passive counterpart (∼0.202γD) in the limit of τa/τr → high. Interestingly, when τa/τr = 1, half the upper bound of excess work is achieved irrespective of the strength of either reservoirs, thermal or active. Finally, we look into the average displacement of active Brownian particles in each feedback cycle, which surpasses its thermal analog due to the broader marginal probability distribution.

Information engine with feedback delay based on a two-level system

An information engine based on a two-level system in contact with a thermal reservoir is studied analytically. The model incorporates delay time between the measurement of the state of the system and the feedback. The engine efficiency and work extracted per cycle are studied as a function of delay time and energy spacing between the two levels. It is found that the range of delay time over which one can extract work from the information engine increases with temperature. For delay times comparable to the relaxation time, efficiency and work per cycle are maxima when k_{B}T≈2U_{0}, the energy difference between the levels. The generalized Jarzynski equality and the generalized integral fluctuation theorem are explicitly verified for the model. The results from the model are compared with the simulation results for a feedback engine based on a particle moving in a one-dimensional square potential. The variation of efficiency, work per cycle, and efficacy with the delay time is compared using relaxation time in the two-level model as the fitting parameter, leading to a good fit.

Geometric Brownian information engine: Essentials for the best performance

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}, the 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 achievable work. 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 extractable 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 crossover from 2 to 11/9. We discover that the condition for the best efficacy depends only on the confinement lengthscale 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.

Driven particle in a one-dimensional periodic potential with feedback control: Efficiency and power optimization

A Brownian particle moving in a staircaselike potential with feedback control offers a way to implement Maxwell's demon. An experimental demonstration of such a system using sinusoidal periodic potential carried out by Toyabe et al. [Nat. Phys. 6, 988 (2010)1745-247310.1038/nphys1821] has shown that information about the particle's position can be converted to useful work. In this paper, we carry out a numerical study of a similar system using Brownian dynamics simulation. A Brownian particle moving in a periodic potential under the action of a constant driving force is made to move against the drive by measuring the position of the particle and effecting feedback control by altering potential. The work is extracted during the potential change and from the movement of the particle against the external drive. These work extractions come at the cost of information gathered during the measurement. Efficiency and work extracted per cycle of this information engine are optimized by varying control parameters as well as feedback protocols. Both these quantities are found to crucially depend on the amplitude of the periodic potential as well as the width of the region over which the particle is searched for during the measurement phase. For the case when potential flip (i.e., changing the phase of the potential by 180^{∘}) is used as the feedback mechanism, we argue that the square potential offers a more efficient information-to-work conversion. The control over the numerical parameters and averaging over large number of trial runs allow one to study the nonequilibrium work relations with feedback for this process with precision. It is seen that the generalized integral fluctuation theorem for error-free measurements holds to within the accuracy of the simulation.

Energy Renewal: Isothermal Utilization of Environmental Heat Energy with Asymmetric Structures

Through the research presented herein, it is quite clear that there are two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A, such as glycolysis and the tricarboxylic acid cycle, apparently follows the second law well; Type B, as exemplified by the thermotrophic function with transmembrane electrostatically localized protons presented here, does not necessarily have to be constrained by the second law, owing to its special asymmetric function. This study now, for the first time, numerically shows that transmembrane electrostatic proton localization (Type-B process) represents a negative entropy event with a local protonic entropy change (ΔSL) in a range from -95 to -110 J/K∙mol. This explains the relationship between both the local protonic entropy change (ΔSL) and the mitochondrial environmental temperature (T) and the local protonic Gibbs free energy (ΔGL=TΔSL) in isothermal environmental heat utilization. The energy efficiency for the utilization of total protonic Gibbs free energy (ΔGT including ΔGL=TΔSL) in driving the synthesis of ATP is estimated to be about 60%, indicating that a significant fraction of the environmental heat energy associated with the thermal motion kinetic energy (kBT) of transmembrane electrostatically localized protons is locked into the chemical form of energy in ATP molecules. Fundamentally, it is the combination of water as a protonic conductor, and thus the formation of protonic membrane capacitor, with asymmetric structures of mitochondrial membrane and cristae that makes this amazing thermotrophic feature possible. The discovery of energy Type-B processes has inspired an invention (WO 2019/136037 A1) for energy renewal through isothermal environmental heat energy utilization with an asymmetric electron-gated function to generate electricity, which has the potential to power electronic devices forever, including mobile phones and laptops. This invention, as an innovative Type-B mimic, may have many possible industrial applications and is likely to be transformative in energy science and technologies for sustainability on Earth.

Isothermal Environmental Heat Energy Utilization by Transmembrane Electrostatically Localized Protons at the Liquid-Membrane Interface

This study employing the latest theory on transmembrane electrostatic proton localization has now, for the first time, consistently elucidated a decades-longstanding bioenergetic conundrum in alkalophilic bacteria and more importantly discovered an entirely new feature: isothermal environmental heat utilization by electrostatically localized protons at the liquid-membrane interface. It was surprisingly revealed that the protonic motive force (equivalent to Gibbs free energy) from the isothermal environmental heat energy utilization through the electrostatically localized protons is not constrained by the overall energetics of the redox-driven proton pump system because of the following: (a) the transmembrane electrostatically localized protons are not free to move away from the membrane surface as a protonic capacitor feature; (b) the proton pumps embedded in the cell membrane extend beyond the localized proton layer apparently as an asymmetric property of the biological membrane; and (c) the protonic inlet mouth of the ATP synthase that accepts protons is located within this layer as another natural property of the asymmetric biological membrane. This work has now, for the first time, shown a novel thermotrophic feature where biological systems can isothermally utilize environmental heat energy through transmembrane electrostatically localized protons to help drive ATP synthesis.

An experimentally-achieved information-driven Brownian motor shows maximum power at the relaxation time

We present an experimental realization of an information-driven Brownian motor by periodically cooling a Brownian particle trapped in a harmonic potential connected to a single heat bath, where cooling is carried out by the information process consisting of measurement and feedback control. We show that the random motion of the particle is rectified by symmetry-broken feedback cooling where the particle is cooled only when it resides on the specific side of the potential center at the instant of measurement. Studying how the motor thermodynamics depends on cycle period τ relative to the relaxation time τ_B of the Brownian particle, we find that the ratcheting of thermal noise produces the maximum work extraction when τ ≥ 5τ_B, while the extracted power is maximum near τ = τ_B, implying the optimal operating time for the ratcheting process. In addition, we find that the average transport velocity is monotonically decreased as τ increases and present the upper bound for the velocity.

Extracting work from a single reservoir in the non-Markovian underdamped regime

We derive optimal-work finite time protocols for a colloidal particle in a harmonic well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal-work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behavior of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quasistatic processes. When measurements are performed, protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below that predicted by Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements.

Optimal tuning of a confined Brownian information engine

A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ. We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.

Resonance behavior of a charged particle in presence of a time dependent magnetic field

In this article, we have explored the resonance behavior of a particle in the presence of a time dependent magnetic field (TDMF). The particle is bound in a harmonic potential well. Based on the Hamiltonian description of the system in terms of action and angle variables, we have derived the resonance condition for the applied TDMF along z-direction which is valid for arbitrary frequencies along x and y directions of the two dimensional harmonic oscillator. We have also derived resonance condition for the applied magnetic field which is lying in a plane. Finally, we have explored resonance condition for the isotropic magnetic field. To check the validity of the theoretical calculation, we have solved equations of motion numerically for the parameter sets which satisfy the derived resonance condition. The numerical experiment fully agrees with the theoretically derived resonance conditions.

Realization of nonequilibrium thermodynamic processes using external colored noise

We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey the Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen.