Experimental Realization of an Information Machine with Tunable Temporal Correlations

Efficiency at Maximum Power of a Carnot Quantum Information Engine

Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.

Dynamics of a colloidal particle driven by continuous time-delayed feedback

We perform feedback experiments and simulations in which a colloidal dumbbell particle, acting as a particle on a ring, is followed by a repulsive optical trap controlled by a continuous-time-delayed feedback protocol. The dynamics are described by a persistent random walk similarly to that of an active Brownian particle, with a transition from predominantly diffusive to driven behavior at a critical delay time. We model the dynamics in the short and long delay regimes using stochastic delay differential equations and derive a condition for stable driven motion. We study the stochastic thermodynamic properties of the system, finding that the maximum work done by the trap coincides with a local minimum in the mutual information between the trap and the particle position at the onset of stable driven dynamics.

Generalized continuous Maxwell demons

We introduce a family of generalized continuous Maxwell demons (GCMDs) operating on idealized single-bit equilibrium devices that combine the single-measurement Szilard and the repeated measurements of the continuous Maxwell demon protocols. We derive the cycle distributions for extracted work, information content, and time and compute the power and information-to-work efficiency fluctuations for the different models. We show that the efficiency at maximum power is maximal for an opportunistic protocol of continuous type in the dynamical regime dominated by rare events. We also extend the analysis to finite-time work extracting protocols by mapping them to a three-state GCMD. We show that dynamical finite-time correlations in this model increase the information-to-work conversion efficiency, underlining the role of temporal correlations in optimizing information-to-energy conversion. The effect of finite-time work extraction and demon memory resetting is also analyzed. We conclude that GCMD models are thermodynamically more efficient than the single-measurement Szilard and preferred for describing biological processes in an information-redundant world.

Bayesian Information Engine that Optimally Exploits Noisy Measurements

We have experimentally realized an information engine consisting of an optically trapped, heavy bead in water. The device raises the trap center after a favorable "up" thermal fluctuation, thereby increasing the bead's average gravitational potential energy. In the presence of measurement noise, poor feedback decisions degrade its performance; below a critical signal-to-noise ratio, the engine shows a phase transition and cannot store any gravitational energy. However, using Bayesian estimates of the bead's position to make feedback decisions can extract gravitational energy at all measurement noise strengths and has maximum performance benefit at the critical signal-to-noise ratio.

Colossal Power Extraction from Active Cyclic Brownian Information Engines

Brownian information engines can extract work from thermal fluctuations by utilizing information. To date, the studies on Brownian information engines consider the system in a thermal bath; however, many processes in nature occur in a nonequilibrium setting, such as the suspensions of self-propelled microorganisms or cellular environments called an active bath. Here, we introduce an archetypal model for a Maxwell-demon type cyclic Brownian information engine operating in a Gaussian correlated active bath capable of extracting more work than its thermal counterpart. We obtain a general integral fluctuation theorem for the active engine that includes additional mutual information gained from the active bath with a unique effective temperature. This effective description modifies the generalized second law and provides a new upper bound for the extracted work. Unlike the passive information engine operating in a thermal bath, the active information engine extracts colossal power that peaks at the finite cycle period. Our study provides fundamental insights into the design and functioning of synthetic and biological submicrometer motors in active baths under measurement and feedback control.

Maximal fluctuation exploitation in Gaussian information engines

Understanding the connections between information and thermodynamics has been among the most visible applications of stochastic thermodynamics. While recent theoretical advances have established that the second law of thermodynamics sets limits on information-to-energy conversion, it is currently unclear to what extent real systems can achieve the predicted theoretical limits. Using a simple model of an information engine that has recently been experimentally implemented, we explore the limits of information-to-energy conversion when an information engine's benefit is limited to output energy that can be stored. We find that restricting the engine's output in this way can limit its ability to convert information to energy. Nevertheless, a feedback control that inputs work can allow the engine to store energy at the highest achievable rate. These results sharpen our theoretical understanding of the limits of real systems that convert information to energy.

Dichotomous flow with thermal diffusion and stochastic resetting

We consider properties of one-dimensional diffusive dichotomous flow and discuss effects of stochastic resonant activation (SRA) in the presence of a statistically independent random resetting mechanism. Resonant activation and stochastic resetting are two similar effects, as both of them can optimize the noise-induced escape. Our studies show completely different origins of optimization in adapted setups. Efficiency of stochastic resetting relies on elimination of suboptimal trajectories, while SRA is associated with matching of time scales in the dynamic environment. Consequently, both effects can be easily tracked by studying their asymptotic properties. Finally, we show that stochastic resetting cannot be easily used to further optimize the SRA in symmetric setups.

Optimal work extraction and mutual information in a generalized Szilárd engine

A 1929 Gedankenexperiment proposed by Szilárd, often referred to as "Szilárd's engine", has served as a foundation for computing fundamental thermodynamic bounds to information processing. While Szilárd's original box could be partitioned into two halves and contains one gas molecule, we calculate here the maximal average work that can be extracted in a system with N particles and q partitions, given an observer which counts the molecules in each partition, and given a work extraction mechanism that is limited to pressure equalization. We find that the average extracted work is proportional to the mutual information between the one-particle position and the vector containing the counts of how many particles are in each partition. We optimize this quantity over the initial locations of the dividing walls, and find that there exists a critical number of particles N^{★}(q) below which the extracted work is maximized by a symmetric configuration of the q partitions, and above which the optimal partitioning is asymmetric. Overall, the average extracted work is maximized for a number of particles N[over ̂](q)<N^{★}(q), with a symmetric partition. We calculate asymptotic values for N→∞.

Maximizing power and velocity of an information engine

Information-driven engines that rectify thermal fluctuations are a modern realization of the Maxwell-demon thought experiment. We introduce a simple design based on a heavy colloidal particle, held by an optical trap and immersed in water. Using a carefully designed feedback loop, our experimental realization of an "information ratchet" takes advantage of favorable "up" fluctuations to lift a weight against gravity, storing potential energy without doing external work. By optimizing the ratchet design for performance via a simple theory, we find that the rate of work storage and velocity of directed motion are limited only by the physical parameters of the engine: the size of the particle, stiffness of the ratchet spring, friction produced by the motion, and temperature of the surrounding medium. Notably, because performance saturates with increasing frequency of observations, the measurement process is not a limiting factor. The extracted power and velocity are at least an order of magnitude higher than in previously reported engines.

Measurements and characterization of the dynamics of tracer particles in an actin network

The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.

Autonomous out-of-equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations

An autonomous out-of-equilibrium Maxwell's demon is used to reverse the natural direction of the heat flux between two electric circuits kept at different temperatures and coupled by the electric thermal noise. The demon does not process any information, but it achieves its goal by using a frequency-dependent coupling with the two reservoirs of the system. There is no mean energy flux between the demon and the system, but the total entropy production (system+demon) is positive. The demon can be power supplied by thermocouples. The system and the demon are ruled by equations similar to those of two coupled Brownian particles and of the Brownian gyrator. Thus our results pave the way to the application of autonomous out-of-equilibrium Maxwell's demons to coupled nanosystems at different temperatures.

Variations on a demonic theme: Szilard's other engines

Szilard's now-famous single-molecule engine was only the first of three constructions he introduced in 1929 to resolve several challenges arising from Maxwell's demon paradox. Given that it has been thoroughly analyzed, we analyze Szilard's remaining two demon models. We show that the second one, though a markedly different implementation employing a population of distinct molecular species and semipermeable membranes, is informationally and thermodynamically equivalent to an ideal gas of the single-molecule engines. One concludes that (i) it reduces to a chaotic dynamical system-called the Szilard Map, a composite of three piecewise linear maps and associated thermodynamic transformations that implement measurement, control, and erasure; (ii) its transitory functioning as an engine that converts disorganized heat energy to work is governed by the Kolmogorov-Sinai entropy rate; (iii) the demon's minimum necessary "intelligence" for optimal functioning is given by the engine's statistical complexity; and (iv) its functioning saturates thermodynamic bounds and so it is a minimal, optimal implementation. We show that Szilard's third construction is rather different and addresses the fundamental issue raised by the first two: the link between entropy production and the measurement task required to implement either of his engines. The analysis gives insight into designing and implementing novel nanoscale information engines by investigating the relationships between the demon's memory, the nature of the "working fluid," and the thermodynamic costs of erasure and measurement.

Information ratchet with time-varying temperature

We discuss a thermodynamic process with information and justify a general form of fluctuation relation. It shows that the fluctuation relation is valid whatever it is the temperature or Hamiltonian that drives the system out of equilibrium state. Based on the stochastic equation we obtain a nonequilibrium equality that involves both information and time-varying temperature. Through the processing of a harmonic system we demonstrate the validity of the equality by converting information into work. We also discuss the general second law of thermodynamics with time-varying temperature and verify its validity in an example by using information to reduce the total entropy.

Work Fluctuations and Jarzynski Equality in Stochastic Resetting

We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle also experiences intermittent long jumps that reset the particle back at a preferred location. Due to the modulation of the trap, work is done on the system and we investigate the statistical properties of the work fluctuations. We find that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event. When observed for a finite time, we show that the system does not generically obey the Jarzynski equality that connects the finite time work fluctuations to the difference in free energy. Nonetheless, we identify herein a restricted set of protocols which embraces the relation. In stark contrast, the Jarzynski equality is always fulfilled when the protocols continue to evolve without being reset. We present a set of exactly solvable models, demonstrate the validation of our theory and carry out numerical simulations to illustrate these findings. Finally, we have pointed out possible realistic implementations for resetting in experiments using the so-called engineered swift equilibration.

Thermodynamic Cost and Benefit of Memory

This Letter exposes a tight connection between the thermodynamic efficiency of information processing and predictive inference. A generalized lower bound on dissipation is derived for partially observable information engines which are allowed to use temperature differences. It is shown that the retention of irrelevant information limits efficiency. A data representation method is derived from optimizing a fundamental physical limit to information processing: minimizing the lower bound on dissipation leads to a compression method that maximally retains relevant, predictive, information. In that sense, predictive inference emerges as the strategy that least precludes energy efficiency.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.