Stochastic thermodynamics, fluctuation theorems and molecular machines

1/ f noise from the laws of thermodynamics for finite-size fluctuations

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual way to resolve Gibbs' paradox that avoids entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for 1/f noise comes from assuming that finite-size fluctuations strictly obey the laws of thermodynamics, even in small parts of a large system. Empirical evidence for the model comes from its ability to match the measured temperature dependence of the spectral-density exponents in several metals and to show non-Gaussian fluctuations characteristic of nanoscale systems.

Note: Three-dimensional linearization of optical trap position detection for precise high speed diffusion measurements

Studies of the details of Brownian motion, hydrodynamic of colloids, or protein diffusion measurements all require high temporal and spatial resolution of the position detector and a means to trap the colloid. Optical trap based thermal noise imaging employing a quadrant photodiode as detector provides such a method. However, optical trapping requires an objective with high numerical aperture resulting in highly nonlinear position signal and significant cross-dependence of the three spatial directions. Local diffusion measurements are especially susceptible to distance errors. Here, we present a position calibration method, which corrects nonlinearities sufficiently to allow precise local diffusion measurement throughout the entire trapping volume. This correction permits us to obtain high-resolution two- and three-dimensional diffusion maps.

Energy pumping in electrical circuits under avalanche noise

We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasistatic and finite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.

Operations and thermodynamics of an artificial rotary molecular motor in solution

A general framework is provided that makes possible the estimation of time-dependent properties of a stochastic system moving far from equilibrium. The process is investigated and discussed in general terms of nonequilibrium thermodynamics. The approach is simple and can be exploited to gain insight into the dynamics of any molecular-level machine. As a case study, the dynamics of an artificial molecular rotary motor, similar to the inversion of a helix, which drives the motor from a metastable state to equilibrium, are examined. The energy path that the motor walks was obtained from the results of atomistic calculations. The motor undergoes unidirectional rotation and its entropy, internal energy, free energy, and net exerted force are given as a function of time, starting from the solution of Smoluchowski's equation. The rather low value of the organization index, that is, the ratio of the work done by the particle against friction during the unidirectional motion per available free energy, reveals that the motion is mainly subject to randomness, and the amount of energy converted to heat due to the directional motion is very small.

Dynamic phase transitions in simple driven kinetic networks

We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, where energy fluxes typically result in nonequilibrium dynamics. By analyzing the fluctuations in the entropy production, we demonstrate the emergence, in a large system size limit, of a dynamic phase transition between two distinct dynamical regimes.

Stochastic functionals and fluctuation theorem for multikangaroo processes

We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.

Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise

For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear response function in terms of the velocity correlation functions is derived by applying the method developed for nonequilibrium Langevin systems [Harada and Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. We verify numerically for the shell-model case that the derived expression of the response function, as the noise tends to zero, converges to the response function of the noiseless shell model.

Boltzmann distribution in a nonequilibrium steady state: measuring local potential by granular Brownian particles

We investigate experimentally the steady state motion of a millimeter-sized granular polyhedral object on vertically vibrating platforms of flat, conical, and parabolic surfaces. We find that the position distribution of the granular object is related to the shape of the platform, just like that of a Brownian particle trapped in a potential at equilibrium, even though the granular object is intrinsically not at equilibrium due to inelastic collisions with the platform. From the collision dynamics, we derive the Langevin equation which describes the motion of the object under an effective potential that equals the gravitational potential along the platform surface. The potential energy is found to agree with the equilibrium equipartition theorem while the kinetic energy does not. Furthermore, the granular temperature is found to be higher than the effective temperature associated with the average potential energy, suggesting the presence of heat transfer from the kinetic part to the potential part of the granular object.

Nonequilibrium work relation beyond the Boltzmann-Gibbs distribution

The presence of multiplicative noise can alter measurements of forces acting on nanoscopic objects. Taking into account of multiplicative noise, we derive a series of nonequilibrium thermodynamical equalities as generalization of the Jarzynski equality, the detailed fluctuation theorem and the Hatano-Sasa relation. Our result demonstrates that the Jarzynski equality and the detailed fluctuation theorem remains valid only for systems with the Boltzmann-Gibbs distribution at the equilibrium state, but the Hatano-Sasa relation is robust with respect to different stochastic interpretations of multiplicative noise.

Unfolding kinetics of periodic DNA hairpins

DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-grained free energy landscape (FEL) as a function of the number of open base pairs and applied mechanical force. Using a commonly employed model, we first analyze for which types of sequences a particularly simple landscape structure is predicted, where forward and backward energy barriers between partly unfolded states are decreasing linearly with force. Stochastic unfolding trajectories for such molecules with simple FEL are subsequently generated by kinetic Monte Carlo simulations. Introducing probabilities that can be sampled from these trajectories, it is shown how the parameters characterizing the FEL can be estimated. Already 300 trajectories, as typically generated in experiments, provide faithful results for the FEL parameters.

Energy versus information based estimations of dissipation using a pair of magnetic colloidal particles

Using the framework of stochastic thermodynamics, we present an experimental study of a doublet of magnetic colloidal particles that is manipulated by a time-dependent magnetic field. Because of hydrodynamic interactions, each bead experiences a state-dependent friction, which we characterize using a hydrodynamic model. In this work, we compare two estimates of the dissipation in this system: the first one is energy based since it relies on the measured interaction potential, while the second one is information based since it uses only the information content of the trajectories. While the latter only offers a lower bound of the former, we find it to be simple to implement and of general applicability to more complex systems.

Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control

Continuous feedback control of Langevin processes may be non-Markovian due to a time lag between the measurement and the control action. We show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process. We then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state, which can also be regarded as the trajectory-dependent total entropy production. This leads to an extension of the second law, which takes a simple form in the long-time limit. As an illustration, we apply the general approach to linear systems that are both analytically tractable and experimentally relevant.

Flight-crash events in turbulence

The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales.

Delay-induced transport in a rocking ratchet under feedback control

Based on the Fokker-Planck equation we investigate the transport of an overdamped colloidal particle in a static, asymmetric periodic potential supplemented by a time-dependent, delayed feedback force, F(fc). For a given time t, F(fc) depends on the status of the system at a previous time t-τ(D), with τ(D) being a delay time, specifically on the delayed mean particle displacement (relative to some "switching position"). For nonzero delay times F(fc)(t) develops nearly regular oscillations, generating a net current in the system. Depending on the switching position, this current is nearly as large or even larger than that in a conventional open-loop rocking ratchet. We also investigate thermodynamic properties of the delayed nonequilibrium system and we suggest an underlying Langevin equation which reproduces the Fokker-Planck results.

Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we demonstrate experimentally the validity of a fluctuation theorem for the relative entropy change occurring during relaxation from a non-equilibrium steady state. The platform established here allows non-equilibrium fluctuation theorems to be studied experimentally for arbitrary steady states and can be extended to investigate quantum fluctuation theorems as well as systems that do not obey detailed balance.

Quantum driving and work

As quantum systems become more experimentally accessible, we are forced to reconsider the notions of control and work to fully account for quantum effects. To this end, we identify the work injected into a quantum system during a general quantum-mechanical driving protocol and quantify the relevant heat flows. The known results that are applicable in the limit of a classical drive are shown to emerge from our equations as a special case. Using the established framework, we show that the Bochkov-Kuzovlev identity for the exclusive work distribution is modified in a nontrivial way by the accumulation of system-drive correlations resulting from quantum back action. Our results accentuate the conceptual and discernible differences between a fully quantum-mechanical and classical driving protocols of quantum systems.

Exact fluctuation theorem without ensemble quantities

Evaluating the entropy production (EP) along a stochastic trajectory requires the knowledge of the system probability distribution, an ensemble quantity notoriously difficult to measure. In this paper we show that the EP of nonautonomous systems in contact with multiple reservoirs can be expressed solely in terms of physical quantities measurable at the single-trajectory level with a suitable preparation of the initial condition. As a result, we identify universal energy and particle fluctuation relations valid for any measurement time. We apply our findings to an electronic junction model, which may be used to verify our prediction experimentally.

Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity

When a Brownian particle in contact with a heat bath at a constant temperature is controlled by a time-dependent harmonic potential, its distribution function can be rigorously derived from the Kramers equation with the consideration of the inertial effect of the Brownian particle. Based on this rigorous solution and the concept of shortcuts to adiabaticity, we construct a stochastic heat engine by employing the time-dependent harmonic potential to manipulate the Brownian particle to complete a thermodynamic cycle. We find that the efficiency at maximum power of this stochastic heat engine is equal to 1-sqrt[T(c)/T(h)], where T(c) and T(h) are the temperatures of the cold bath and the hot one in the thermodynamic cycle, respectively.

Symmetry for the duration of entropy-consuming intervals

We introduce the violation fraction υ as the cumulative fraction of time that a mesoscopic system spends consuming entropy at a single trajectory in phase space. We show that the fluctuations of this quantity are described in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function Φ, which can be interpreted as an entropy associated with the fluctuations of the violation fraction. The function Φ, when evaluated for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations that are relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the probability density function of Φ. We study the steady-state limit of this symmetry in the paradigmatic case of a colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss possible applications of our results for the estimation of free-energy differences from single-molecule experiments.

Optimal finite-time erasure of a classical bit

Information erasure inevitably leads to the generation of heat. Minimizing this dissipation will be crucial for developing small-scale information processing systems, but little is known about the optimal procedures required. We have obtained closed-form expressions for maximally efficient erasure cycles for deletion of a classical bit of information stored by the position of a particle diffusing in a double-well potential. We find that the extra heat generated beyond the Landauer bound is proportional to the square of the Hellinger distance between the initial and final states divided by the cycle duration, which quantifies how far out of equilibrium the system is driven. Finally, we demonstrate close agreement between the exact optimal cycle and the protocol found using a linear response framework.

Generalized energy measurements and modified transient quantum fluctuation theorems

Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.

Nonequilibrium fluctuation-dissipation relations for one- and two-particle correlation functions in steady-state quantum transport

We study the non-equilibrium (NE) fluctuation-dissipation (FD) relations in the context of quantum thermoelectric transport through a two-terminal nanodevice in the steady-state. The FD relations for the one- and two-particle correlation functions are derived for a model of the central region consisting of a single electron level. Explicit expressions for the FD relations of the Green's functions (one-particle correlations) are provided. The FD relations for the current-current and charge-charge (two-particle) correlations are calculated numerically. We use self-consistent NE Green's functions calculations to treat the system in the absence and in the presence of interaction (electron-phonon) in the central region. We show that, for this model, there is no single universal FD theorem for the NE steady state. There are different FD relations for each different class of problems. We find that the FD relations for the one-particle correlation function are strongly dependent on both the NE conditions and the interactions, while the FD relations of the current-current correlation function are much less dependent on the interaction. The latter property suggests interesting applications for single-molecule and other nanoscale transport experiments.

Classical Nernst engine

We introduce a simple model for an engine based on the Nernst effect. In the presence of a magnetic field, a vertical heat current can drive a horizontal particle current against a chemical potential. For a microscopic model invoking classical particle trajectories subject to the Lorentz force, we prove a universal bound 3-2√2≃0.172 for the ratio between the maximum efficiency and the Carnot efficiency. This bound, as the slightly lower one 1/6 for efficiency at maximum power, can indeed be saturated for a large magnetic field and small fugacity.

Nonequilibrium Brownian motion beyond the effective temperature

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein’s relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own “effective” temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein’s relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.

Direct evidence for three-dimensional off-axis trapping with single Laguerre-Gaussian beam

Optical tweezers are often applied to control the dynamics of objects by scanning light. However, there is a limitation that objects fail to track the scan when the drag exceeds the trapping force. In contrast, Laguerre-Gaussian (LG) beams can directly control the torque on objects and provide a typical model for nonequilibrium systems such as Brownian motion under external fields. Although stable “mid-water” trapping is essential for removing extrinsic hydrodynamic effects in such studies, three-dimensional trapping by LG beams has not yet been clearly established. Here we report the three-dimensional off-axis trapping of dielectric spheres using high-quality LG beams generated by a special holographic method. The trapping position was estimated as ~ half the wavelength behind the beam waist. These results establish the scientific groundwork of LG trapping and the technical basis of calibrating optical torque to provide powerful tools for studying energy-conversion mechanisms and the nonequilibrium nature of biological molecules under torque.

Trajectory Entropy of Continuous Stochastic Processes at Equilibrium

We propose to quantify the trajectory entropy of a dynamic system as the information content in excess of a free-diffusion reference model. The space-time trajectory is now the dynamic variable, and its path probability is given by the Onsager-Machlup action. For the time propagation of the overdamped Langevin equation, we solved the action path integral in the continuum limit and arrived at an exact analytical expression that emerged as a simple functional of the deterministic mean force and the stochastic diffusion. This work may have direct implications in chemical and phase equilibria, bond isomerization, and conformational changes in biological macromolecules as well transport problems in general.

Unifying three perspectives on information processing in stochastic thermodynamics

So far, feedback-driven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system, or (iii) by identifying an implicit Maxwell demon in steady-state transport. We derive the corresponding second laws from one master fluctuation theorem and discuss their relationship. In particular, we show that both the entropy production involving mutual information between system and controller and the one involving a Shannon entropy difference of an information reservoir like a tape carry an extra term different from the usual current times affinity. We, thus, generalize stochastic thermodynamics to the presence of an information reservoir.

Roles of dry friction in the fluctuating motion of an adiabatic piston

The motion of an adiabatic piston under dry friction is investigated to clarify the roles of dry friction in nonequilibrium steady states. We clarify that dry friction can reverse the direction of the piston motion and causes a discontinuity or a cusplike singularity for velocity distribution functions of the piston. We also show that the heat fluctuation relation is modified under dry friction.

Duration of local violations of the second law of thermodynamics along single trajectories in phase space

We define the violation fraction ν as the cumulative fraction of time that the entropy change is negative during single realizations of processes in phase space. This quantity depends on both the number of degrees of freedom N and the duration of the time interval τ. In the large-τ and large-N limit we show that, for ergodic and microreversible systems, the mean value of ν scales as 〈ν(N,τ)〉 ∼ (τN(1/1+α))(-1). The exponent α is positive and generally depends on the protocol for the external driving forces, being α = 1 for a constant drive. As an example, we study a nontrivial model where the fluctuations of the entropy production are non-Gaussian: an elastic line driven at a constant rate by an anharmonic trap. In this case we show that the scaling of 〈ν〉 with N and τ agrees with our result. Finally, we discuss how this scaling law may break down in the vicinity of a continuous phase transition.

Role of parity transformation for the fluctuation theorem: limit cycle and symmetry breaking

The fluctuation theorem of the Crooks type is studied for thermodynamic nonlinear-multivariate systems. In particular, a bivariate system having a limit cycle is discussed in detail. It is explicitly shown how the time reversal operation has to be combined with the parity transformation in order to derive the fluctuation theorem for the change of the "renormalized entropy." Furthermore, breakdown of the symmetry in a limit-cycle model due to the effect of fluctuations is also discussed.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here.

Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [ M. Esposito, R. Kawai, K. Lindenberg and C. Van den Broeck Phys. Rev. Lett. 105 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.

Macroscopically deterministic Markovian thermalization in finite quantum spin systems

A key feature of nonequilibrium thermodynamics is the Markovian, deterministic relaxation of coarse observables such as, for example, the temperature difference between two macroscopic objects which evolves independently of almost all details of the initial state. We demonstrate that the unitary dynamics for moderately sized spin-1/2 systems may yield the same type of relaxation dynamics for a given magnetization difference. This observation might contribute to the understanding of the emergence of thermodynamics within closed quantum systems.

Statistics and Related Topics in Single-Molecule Biophysics

Since the universal acceptance of atoms and molecules as the fundamental constituents of matter in the early twentieth century, molecular physics, chemistry and molecular biology have all experienced major theoretical breakthroughs. To be able to actually "see" biological macromolecules, one at a time in action, one has to wait until the 1970s. Since then the field of single-molecule biophysics has witnessed extensive growth both in experiments and theory. A distinct feature of single-molecule biophysics is that the motions and interactions of molecules and the transformation of molecular species are necessarily described in the language of stochastic processes, whether one investigates equilibrium or nonequilibrium living behavior. For laboratory measurements following a biological process, if it is sampled over time on individual participating molecules, then the analysis of experimental data naturally calls for the inference of stochastic processes. The theoretical and experimental developments of single-molecule biophysics thus present interesting questions and unique opportunity for applied statisticians and probabilists. In this article, we review some important statistical developments in connection to single-molecule biophysics, emphasizing the application of stochastic-process theory and the statistical questions arising from modeling and analyzing experimental data.

Large deviation function and fluctuation theorem for classical particle transport

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.

Optimal control of transitions between nonequilibrium steady states

Biological systems fundamentally exist out of equilibrium in order to preserve organized structures and processes. Many changing cellular conditions can be represented as transitions between nonequilibrium steady states, and organisms have an interest in optimizing such transitions. Using the Hatano-Sasa Y-value, we extend a recently developed geometrical framework for determining optimal protocols so that it can be applied to systems driven from nonequilibrium steady states. We calculate and numerically verify optimal protocols for a colloidal particle dragged through solution by a translating optical trap with two controllable parameters. We offer experimental predictions, specifically that optimal protocols are significantly less costly than naive ones. Optimal protocols similar to these may ultimately point to design principles for biological energy transduction systems and guide the design of artificial molecular machines.

Information flow and optimal protocol for a Maxwell-demon single-electron pump

We study the entropy and information flow in a Maxwell-demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages, which minimizes irreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems in which barriers between different regions can be manipulated.

Nonequilibrium heat capacity

Development of steady state thermodynamics and statistical mechanics depends crucially on our ability to extend the notions of equilibrium thermodynamics to nonequilibrium steady states (NESS). The present paper considers the extension of heat capacity. A modified definition is proposed which continues to maintain the same relation to steady state Shannon entropy as in equilibrium, thus providing a thermodynamically consistent treatment of NESS heat capacity.

Kinetic constraints, hierarchical relaxation, and onset of glassiness in strongly interacting and dissipative Rydberg gases

We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the dynamics lead to spatially correlated collective relaxation reminiscent of glasses. We study and quantify the evolution towards equilibrium in one and two dimensions, and analyze how the degree of glassiness and the relaxation time are controlled by the interaction strength between Rydberg atoms. We also find that spontaneous decay of Rydberg excitations leads to an interruption of glassy relaxation that takes the system to a highly correlated nonequilibrium stationary state. The results presented here, which are in principle also applicable to other systems such as polar molecules and atoms with large magnetic dipole moments, show that the collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems.

Nonlinear response in the driven lattice Lorentz gas

We determine the nonlinear time-dependent response of a tracer on a lattice with randomly distributed hard obstacles as a force is switched on. The calculation is exact to first order in the obstacle density and holds for arbitrarily large forces. Whereas, on the impurity-free lattice, the nonlinear drift velocity in the stationary state is analytic in the driving force, interactions with impurities introduce logarithmic contributions beyond the linear regime. The long-time decay of the velocity toward the steady state is exponentially fast for any finite value of the force, in striking contrast to the power-law relaxation predicted within linear response. We discuss the range of validity of our analytic results by comparison to stochastic simulations.

Information thermodynamics on causal networks

We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel generalizations of the second law of thermodynamics and the fluctuation theorem, which include an informational quantity characterized by the topology of the causal network. Our result implies that the entropy production in a single system in the presence of multiple other systems is bounded by the information flow between these systems. We demonstrate our general result by a simple model of biochemical adaptation.

Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect

We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by studying the generalized fluctuation-dissipation relation for this ratchet model driven by Coulomb friction.