arXiv subjects

David A. Sivak

Publications and source records attributed to David A. Sivak.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Control of Periodic Nonequilibrium Mechanochemical Systems via Automatic Differentiation

Biological molecular machines are mesoscopic systems that act repeatedly and periodically to perform important cellular tasks while contending with strong fluctuations and operating in an overdamped regime. Optimal control theory is a tool that can be used to understand the design principles behind efficient operation of these machines; however, most studies on optimal control of classical mesoscopic systems have focused on control problems that do not repeat periodically. Here, we automatically differentiate Fokker-Planck simulations to design efficient nonequilibrium control strategies for simple models of periodic molecular machines with and without explicit changes in the machine's chemical state. The designed protocols and theoretical analysis provide insight into the design principles governing efficient driving in these nonequilibrium systems. Designed control protocols should seek to reduce mechanical heat by rotating the entire angular probability distribution at a constant speed without changing its shape, and should reduce chemical heat by reducing the proportion of chemical transitions with large heat.

cond-mat.stat-mech↗

arXiv2026

Information-driven stepping in dimeric transport motors

Dimeric transport motors are nanoscale protein complexes that move along cytoskeletal filaments. Here we introduce a theoretical model for their stepping dynamics, in which the two motor heads undergo Brownian motion with mobilities periodically switching in a position-dependent manner so that only one head moves at a time. Through consumption of chemical free energy, this mechanism produces directed motion. We characterize at steady state the motor's mean velocity and its energy and information flows. The motor operates as a pure information engine, where only information is transduced between its components, without energy exchange. For localized switching, the model yields a thermodynamically consistent expression for the mean motor velocity that reproduces experimentally observed behavior, and captures the stall force characteristic of tightly coupled motors. Finally, coarse-graining the model to a single mechanical degree of freedom produces a second-order non-Markovian dynamics, from which we compute the four distinct dwell-time distributions that can be directly observed in single-molecule experiments. Our findings highlight how information transduction, via implicit operation as a Maxwell demon, may underlie the remarkable performance of these molecular motors.

physics.bio-ph↗

arXiv2026

Harnessing higher-dimensional fluctuations in an information engine

We study the optimal performance of an information engine consisting of an overdamped Brownian bead confined in a controllable, $d$-dimensional harmonic trap and additionally subjected to gravity. The trap's center is updated dynamically via a feedback protocol designed such that no external work is done by the trap on the bead, while maximizing the extraction of gravitational potential energy and achieving directed motion. We show that performance strikingly improves when thermal fluctuations in directions perpendicular to gravity are harnessed. This improvement arises from feedback cooling of these transverse degrees of freedom, along which all heat is extracted; comparable performance can be achieved even without vertical measurements. This engine design modularizes the functions of harnessing fluctuations and storing free energy, drawing a close analogy to the Szilard engine.

cond-mat.stat-mech↗

arXiv2026

Hunting for Maxwell's Demon in the Wild

The paradox of Maxwell's demon motivated the development of information thermodynamics and the creation of nanoscale information engines. We now understand that machines such as the molecular motors within cells can in principle harvest fluctuations and thereby operate as a Maxwell demon -- but do they? Answering this question would seemingly require simultaneous measurement of all system degrees of freedom, which is generally intractable in single-molecule experiments. Here, we derive a simple statistical estimator to infer both the direction and magnitude of subsystem heat flows, and thus determine whether -- and how strongly -- a motor operates as a Maxwell demon. The estimator uses only trajectory measurements for a single degree of freedom. Simulating both colloidal information engines and kinesin molecular motors, we show that our estimator can precisely and accurately detect Maxwell-demon behavior with experimentally accessible resolution and quantities of data. Moreover, we find that kinesin transitions to a Maxwell-demon mechanism in the presence of nonequilibrium noise, with a corresponding increase in velocity consistent with experiments. These findings suggest that molecular motors may have evolved to leverage active fluctuations within cells.

cond-mat.stat-mech↗

arXiv2026

Information thermodynamics of cellular ion pumps

The framework of bipartite stochastic thermodynamics is a powerful tool to analyze a composite system's internal thermodynamics. It has been used to study the components of different molecular machines such as ATP synthase. However, this approach has not yet been used to describe ion-transporting proteins despite their high-level functional similarity. Here we study the bipartite thermodynamics of the sodium-potassium pump in the nonequilibrium steady state. Using a physically intuitive partition between the ATP-consuming subsystem and the ion-transporting subsystem, we find considerable information flow comparable to other molecular machines, and Maxwell-demon behavior in the ATP-consuming subsystem. We vary ion concentrations and transmembrane voltage in a range including the neuronal action potential, and find that the information flow inverts during depolarization.

cond-mat.stat-mech↗

arXiv2026

Effects of symmetry on coupled rotary molecular motors

As engineering advances toward the nanoscale, understanding design principles for molecular motors becomes increasingly valuable. Many molecular motors consist of coupled components transducing one free-energy source into another. Here, we study the performance of coupled rotary molecular motors with different rotational symmetries under constant and scaling driving forces. Under constant driving and strong coupling, symmetry match between the motors decreases the output power. In contrast, under a scaling driving force, the output power is not sensitive to symmetries. However, driving the upstream motor too strongly reduces the downstream motor's output power, leading to a perhaps counterintuitive phenomenon we term disruption, in which the two motors become disconnected. Across both driving schemes, output power peaks at intermediate coupling, confirming the value of flexible coupling. Beyond providing insights into biological motors, these findings could inform the future design of synthetic nanomotors and structure-based drugs.

cond-mat.stat-mech↗

arXiv2026

Global thermodynamic manifold for conservative control of stochastic systems

Optimal control of stochastic systems plays a central role in nonequilibrium physics, with applications in the study of biological molecular motors and the design of single-molecule experiments. While exact analytic solutions to optimization problems are rare, under slow driving conditions, the problem can be reformulated geometrically solely in terms of equilibrium properties. In this framework, minimum-work protocols are geodesics on a thermodynamic manifold whose metric is a generalized friction tensor. Here, we introduce a new foundation for this friction-tensor formalism for conservatively driven systems. Under complete control of the potential energy, a global thermodynamic manifold (on which points are identified with instantaneous energy landscapes) has as its metric a full-control friction tensor. Arbitrary partial-control friction tensors arise naturally as inherited metrics on submanifolds of this global manifold. Leveraging a simple mathematical relationship between system dynamics and the geometry of the global manifold, we derive new expressions for the friction tensor that offer powerful tools for interpretation and computation of friction tensors and minimum-work protocols. Our results elucidate a connection between relaxation and dissipation in slowly driven systems and suggest optimization heuristics. We demonstrate the utility of these developments in three illustrative examples.

cond-mat.stat-mech↗

arXiv2025

Multiparameter optimal control of F1-ATPase

Biological molecular machines convert free energy between different forms in cells, often at high efficiency. Optimal control theory provides a framework to elucidate design principles governing energetically efficient driving. Here, we use linear-response theory to design efficient protocols exercising dynamic control of trap center and stiffness in a model of driven F1-ATPase. We find that the key design principles of an efficient protocol can be satisfied either by dynamic control of both parameters or by dynamic control of a single parameter and a good static choice for the second. These results illustrate that accessing a new degree of dynamic control provides varying performance improvements in different systems.

physics.bio-ph↗

arXiv2025

Efficiently driving F$_1$ molecular motor in experiment by suppressing nonequilibrium variation

F$_1$-ATPase (F$_1$) is central to cellular energy transduction. Forcibly rotated by another motor F$_\mathrm{o}$, F$_1$ catalyzes ATP synthesis by converting mechanical work into chemical free energy stored in the molecule ATP. The details of how F$_\mathrm{o}$ drives F$_1$ are not fully understood; however, evaluating efficient ways to rotate F$_1$ could provide fruitful insights into this driving since there is a selective pressure to improve efficiency. Here, we show that rotating F$_1$ with an angle clamp is significantly more efficient than a constant torque. Our experiments, combined with theory and simulation, indicate that the angle clamp significantly suppresses the nonequilibrium variation that contributes to the futile dissipation of input work.

physics.bio-ph↗

arXiv2024

Flow of Energy and Information in Molecular Machines

Molecular machines transduce free energy between different forms throughout all living organisms. While truly machines in their own right, unlike their macroscopic counterparts molecular machines are characterized by stochastic fluctuations, overdamped dynamics, and soft components, and operate far from thermodynamic equilibrium. In addition, information is a relevant free-energy resource for molecular machines, leading to new modes of operation for nanoscale engines. Towards the objective of engineering synthetic nanomachines, an important goal is to understand how molecular machines transduce free energy to perform their functions in biological systems. In this review we discuss the nonequilibrium thermodynamics of free-energy transduction within molecular machines, with a focus on quantifying energy and information flows between their components. We review results from theory, modeling, and inference from experiments that shed light on the internal thermodynamics of molecular machines, and ultimately explore what we can learn from considering these interactions.

cond-mat.stat-mech↗

arXiv2024

Information Arbitrage in Bipartite Heat Engines

Heat engines and information engines have each historically served as motivating examples for the development of thermodynamics. While these two types of systems are typically thought of as two separate kinds of machines, recent empirical studies of specific systems have hinted at possible connections between the two. Inspired by molecular machines in the cellular environment, which in many cases have separate components in contact with distinct sources of fluctuations, we study bipartite heat engines. We show that a bipartite heat engine can only produce net output work by acting as an information engine. Conversely, information engines can only extract more work than the work consumed to power them if they have access to different sources of fluctuations, i.e., act as heat engines. We illustrate these findings first through an analogy to economics and a cyclically controlled 2D ideal gas. We then explore two analytically tractable model systems in more detail: a Brownian-gyrator heat engine which we show can be reinterpreted as a feedback-cooling information engine, and a quantum-dot information engine which can be reinterpreted as a thermoelectric heat engine. Our results suggest design principles for both heat engines and information engines at the nanoscale, and ultimately imply constraints on how free-energy transduction is carried out in biological molecular machines.

cond-mat.stat-mech↗

arXiv2024

Performance limits of information engines

We review recent studies of a colloidal information engine that consists of a bead in water and held by an optical trap. The bead is ratcheted upward without any apparent external work, by taking advantage of favorable thermal fluctuations. Much of the previous work on such engines aimed to show that accounting for information-processing costs can reconcile the observed motion with the second law of thermodynamics. By contrast, we focus on the factors that limit the performance of such engines by optimizing variously the upward velocity, rate of gravitational free-energy extraction, or ability to track a trajectory. We then consider measurement noise, which degrades engine performance. A naive use of noisy measurements in the feedback algorithm leads to a phase transition at finite signal-to-noise ratio: below the transition, the engine no longer functions. A more sophisticated, `Bayesian' algorithm eliminates the phase transition and improves performance. Finally, operating the information engine in a nonequilibrium environment with extra force fluctuations can enhance the performance by orders of magnitude, even to the point where the energy extracted exceeds that needed to run the information processing. Autonomous implementations of an information engine in such environments could be powered entirely by the additional energy of the bath.

cond-mat.stat-mech↗

arXiv2023

Information thermodynamics of transition paths between multiple mesostates

A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal asymmetry of the ensemble of such transition paths and the informativeness of system dynamics about the reactivity of a given trajectory, immediately leading to quantitative criteria for judging the importance of distinct system coordinates for the transition. Here we generalize this framework to multiple mesostates. We find that the main system-wide and coordinate-specific results generalize intuitively, while the combinatorial diversity of pairwise transitions raises new questions and points to new concepts. This work increases the previous framework's generality and applicability and forges connections to enhanced-sampling and coarse-grained dynamical approaches such as milestoning and Markov-state models.

cond-mat.stat-mech↗

arXiv2023

Jensen bound for the entropy production rate in stochastic thermodynamics

Bounding and estimating entropy production has long been an important goal of nonequilibrium thermodynamics. We recently derived a lower bound on the total and subsystem entropy production rates of continuous stochastic systems. This `Jensen bound' has led to fundamental limits on the performance of collective transport systems and permitted thermodynamic inference of free-energy transduction between components of bipartite molecular machines. Our original derivation relied on a number of assumptions, which restricted the bound's regime of applicability. Here we derive the Jensen bound far more generally for multipartite overdamped Langevin dynamics. We then consider several extensions, allowing for position-dependent diffusion coefficients, underdamped dynamics, and non-multipartite overdamped dynamics. Our results extend the Jensen bound to a far broader class of systems.

cond-mat.stat-mech↗

arXiv2023

Efficient control protocols for an active Ornstein-Uhlenbeck particle

Designing a protocol to efficiently drive a stochastic system is an active field of research. Here we extend such control theory to an active Ornstein-Uhlenbeck particle (AOUP) in a bistable potential, driven by a harmonic trap. We find that protocols designed to minimize the excess work (up to linear-response) perform better than naive protocols with constant velocity for a wide range of protocol durations.

cond-mat.stat-mech↗

arXiv2023

Signal in the noise: temporal variation in exponentially growing populations

In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of exponential growth we show power-law relationships that relate variability in the time required to reach a threshold population size to growth rate and inoculum size. Population-growth experiments in E. coli and S. aureus with inoculum sizes ranging between 1 and 100 are consistent with these relationships. We quantify how noise accumulates over time, finding that it encodes -- and can be used to deduce -- information about the early growth rate of a population.

q-bio.PE↗

arXiv2023

Inferring Subsystem Efficiencies in Bipartite Molecular Machines

Molecular machines composed of coupled subsystems transduce free energy between different external reservoirs, in the process internally transducing energy and information. While subsystem efficiencies of these molecular machines have been measured in isolation, less is known about how they behave in their natural setting when coupled together and acting in concert. Here we derive upper and lower bounds on the subsystem efficiencies of a bipartite molecular machine. We demonstrate their utility by estimating the efficiencies of the $\mathrm{F}_\mathrm{o}$ and $\mathrm{F}_1$ subunits of ATP synthase and that of kinesin pulling a diffusive cargo.

cond-mat.stat-mech↗

arXiv2023

Energetic cost of feedback control

Successful feedback control of small systems allows for the rectification of thermal fluctuations, converting them into useful energy; however, control itself requires work. This paper emphasizes the fact that the controller is a physical entity interacting with the feedback-controlled system. For a specifically designed class of controllers, reciprocal interactions become nonreciprocal due to large timescale separation, which considerably simplifies the situation. We introduce a minimally dissipative controller model, illustrating the findings using a simple example. We find that the work required to run the controller must at least compensate for the decrease in entropy due to the control operation.

cond-mat.stat-mech↗