Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics.

Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.

Quantum Fokker-Planck Master Equation for Continuous Feedback Control.

Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Theoretical descriptions of feedback control are typically given in terms of stochastic equations requiring numerical solutions, or are limited to linear feedback protocols. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment. We illustrate our formalism by investigating two basic information engines, one quantum and one classical.

Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources.

Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system's initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists.

Shortcuts to Thermodynamic Computing: The Cost of Fast and Faithful Information Processing.

Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature, Boltzmann's constant, and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations-that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allow for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as the square of the information-storing system's length scale. As a paradigmatic example, we design shortcuts to create, erase, and transfer a bit of information metastably stored in a double-well potential. Though dissipated work generally increases with operation fidelity, we show that it is possible to compute with perfect fidelity in finite time with finite work. We also show that the robustness of information storage affects an operation's energetic cost-specifically, the dissipated work scales as the information lifetime of the bistable system. Our analysis exposes a rich and nuanced relationship between work, speed, size of the information-bearing degrees of freedom, storage robustness, and the difference between initial and final informational statistics.

From a feedback-controlled demon to an information ratchet in a double quantum dot.

We present a simple strategy for constructing an information ratchet or memory-tape model of Maxwell's demon, from a feedback-controlled model. We illustrate our approach by converting the Annby-Andersson feedback-controlled double quantum dot model [Phys. Rev. B 101, 165404 (2020)2469-995010.1103/PhysRevB.101.165404] to a memory-tape model. We use the underlying network structure of the original model to design a set of bit interaction rules for the information ratchet. The new model is solved analytically in the limit of long interaction times. For finite-time interactions, semianalytical phase diagrams of operational modes are obtained. Stochastic simulations are used to verify theoretical results.

Understanding cytoskeletal avalanches using mechanical stability analysis.

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model.

Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs-one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template.

Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving.

We study the energy dynamics of a particle in a billiard subject to a rapid periodic drive. In the regime of large driving frequencies ω, we find that the particle's energy evolves diffusively, which suggests that the particle's energy distribution η(E,t) satisfies a Fokker-Planck equation. We calculate the rates of energy absorption and diffusion associated with this equation, finding that these rates are proportional to ω^{-2} for large ω. Our analysis suggests three phases of energy evolution: Prethermalization on short timescales, then slow energy absorption in accordance with the Fokker-Planck equation, and finally a breakdown of the rapid driving assumption for large energies and high particle speeds. We also present numerical simulations of the evolution of a rapidly driven billiard particle, which corroborate our theoretical results.

Recovery of Equilibrium Free Energy from Nonequilibrium Thermodynamics with Mechanosensitive Ion Channels in E. coli.

In situ measurements of the free energy difference between the open and closed states of ion channels are challenging due to hysteresis effects and inactivation. Exploiting recent developments in statistical physics, we present a general formalism to extract the free energy difference ΔF between the closed and open states of mechanosensitive ion channels from nonequilibrium work distributions associated with the opening and closing of the channels (gating) in response to ramp stimulation protocols recorded in native patches. We show that the work distributions obtained from the gating of MscS channels in E. coli membrane satisfy the strong symmetry relation predicted by the Crooks fluctuation theorem. Our approach enables the determination of ΔF using patch-clamp experiments, which are often inherently restricted to the nonequilibrium regime.

Gibbs free energy change of a discrete chemical reaction event.

In modeling the interior of cells by simulating a reaction-diffusion master equation over a grid of compartments, one employs the assumption that the copy numbers of various chemical species are small, discrete quantities. We show that, in this case, textbook expressions for the change in Gibbs free energy accompanying a chemical reaction or diffusion between adjacent compartments are inaccurate. We derive exact expressions for these free energy changes for the case of discrete copy numbers and show how these expressions reduce to traditional expressions under a series of successive approximations leveraging the relative sizes of the stoichiometric coefficients and the copy numbers of the solutes and solvent. Numerical results are presented to corroborate the claim that if the copy numbers are treated as discrete quantities, then only these more accurate expressions lead to correct behavior. Thus, the newly derived expressions are critical for correctly computing entropy production in mesoscopic simulations based on the reaction-diffusion master equation formalism.

Processivity, Velocity, and Universal Characteristics of Nucleic Acid Unwinding by Helicases.

Helicases are components of the cellular replisome that are essential for unwinding double-strand nucleic acids during the process of replication. Intriguingly, most helicases are inefficient and require either oligomerization or assistance from other partner proteins to increase the processivity of unwinding in the presence of the replication fork, which acts as a barrier to progress. Single-molecule force spectroscopy has emerged as a promising experimental technique to probe how relieving this barrier on the helicase can allow for increased efficiency of unwinding. However, there exists no comprehensive theoretical framework to provide unique interpretations of the underlying helicase kinetics from the force spectroscopy data. This remains a major confounding issue in the field. Here, we develop a mathematical framework and derive analytic expressions for the velocity and run length of a general model of finitely processive helicases, the two most commonly measured experimental quantities. We show that in contrast to the unwinding velocity, the processivity exhibits a universal increase in response to external force, irrespective of the underlying architecture and unwinding kinetics of the helicase. Our work provides the first, to our knowledge, explanation to a wide array of experiments and suggests that helicases may have evolved to maximize processivity rather than speed. To demonstrate the use of our theory on experimental data, we analyze velocity and processivity data on the T7 helicase and provide unique inferences on the kinetics of the helicase. Our results show that T7 is a weakly active helicase that destabilizes the fork ahead by less than 1 kBT and back steps very frequently while unwinding DNA. Our work generates fundamental insights into the force response of helicases and provides a widely applicable method for inferring the underlying helicase kinetics from force spectroscopy data.

Optimal Probabilistic Work Extraction beyond the Free Energy Difference with a Single-Electron Device.

We experimentally realize protocols that allow us to extract work beyond the free energy difference from a single-electron transistor at the single thermodynamic trajectory level. With two carefully designed out-of-equilibrium driving cycles featuring kicks of the control parameter, we demonstrate work extraction up to large fractions of k_{B}T or with probabilities substantially greater than 1/2, despite the zero free energy difference over the cycle. Our results are explained in the framework of nonequilibrium fluctuation relations. We thus show that irreversibility can be used as a resource for optimal work extraction even in the absence of feedback from an external operator.

Quantifying dissipation in actomyosin networks.

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

A Programmable Mechanical Maxwell's Demon.

We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon-a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere, but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of π . If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously performs a conversion between information and energy, or else as a feedback-controlled device that is operated by an external agent. We derive generalized second laws of thermodynamics for both pictures. We illustrate our model with numerical simulations, as well as analytical calculations in a particular, exactly solvable limit.

Nonconservative Forces via Quantum Reservoir Engineering.

A systematic approach is given for engineering dissipative environments that steer quantum wave packets along desired trajectories. The methodology is demonstrated with several illustrative examples: environment-assisted tunneling, trapping, effective mass assignment, and pseudorelativistic behavior. Nonconservative stochastic forces do not inevitably lead to decoherence-we show that purity can be well preserved. These findings highlight the flexibility offered by nonequilibrium open quantum dynamics.

Fast forward to the classical adiabatic invariant.

We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H=p^{2}/2m+U(q,t) in one degree of freedom, and for an arbitrary choice of action I_{0}, we construct a so-called fast-forward potential energy function V_{FF}(q,t) that, when added to H, guides all trajectories with initial action I_{0} to end with the same value of action. We use this result to construct a local dynamical invariant J(q,p,t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.

Classical and Quantum Shortcuts to Adiabaticity in a Tilted Piston.

Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian, HCD, is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian, HCD, ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions, or translations of the system. Here we investigate an example of a non-scale-invariant system, a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian, HCD(q, p, t), which we then quantize to obtain a Hermitian operator, HCD(t). Using numerical simulations, we find that HCD effectively suppresses nonadiabatic excitations under rapid driving. These results offer a proof of principle, beyond the special case of scale-invariant driving, that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.

Number of trials required to estimate a free-energy difference, using fluctuation relations.

The difference ΔF between free energies has applications in biology, chemistry, and pharmacology. The value of ΔF can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a ΔF estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly by Jarzynski [Phys. Rev. E 73, 046105 (2006)PLEEE81539-375510.1103/PhysRevE.73.046105]. We enhance the approximation with the following information-theoretic strategies. We quantify "dominance" with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-∞ Rényi entropy. The bound can be estimated if one implements the "good practice" of bidirectionality, known to improve estimates of ΔF. Estimating ΔF from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.

Conditional reversibility in nonequilibrium stochastic systems.

For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate σ, is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, -σ, where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.

Universal energy diffusion in a quivering billiard.

We introduce and study a model of time-dependent billiard systems with billiard boundaries undergoing infinitesimal wiggling motions. The so-called quivering billiard is simple to simulate, straightforward to analyze, and is a faithful representation of time-dependent billiards in the limit of small boundary displacements. We assert that when a billiard's wall motion approaches the quivering motion, deterministic particle dynamics become inherently stochastic. Particle ensembles in a quivering billiard are shown to evolve to a universal energy distribution through an energy diffusion process, regardless of the billiard's shape or dimensionality, and as a consequence universally display Fermi acceleration. Our model resolves a known discrepancy between the one-dimensional Fermi-Ulam model and the simplified static wall approximation. We argue that the quivering limit is the true fixed wall limit of the Fermi-Ulam model.