Showing papers by "Udo Seifert published in 2016"
TL;DR: The authors' bounds provide a general class of constraints for nonequilibrium systems and show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle.
Abstract: For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.
243 citations
TL;DR: The total entropy production is shown to obey an integral fluctuation theorem on the trajectory level implying the second law in the form of a Clausius inequalilty on the ensemble level.
Abstract: For a small driven system coupled strongly to a heat bath, internal energy and exchanged heat are identified such that they obey the usual additive form of the first law. By identifying this exchanged heat with the entropy change of the bath, the total entropy production is shown to obey an integral fluctuation theorem on the trajectory level implying the second law in the form of a Clausius inequalilty on the ensemble level. In this Hamiltonian approach, the assumption of an initially uncorrelated state is not required. The conditions under which the proposed identification of heat is unique and experimentally accessible are clarified.
182 citations
TL;DR: It is shown that a clock driven by a periodic variation of an external protocol can achieve arbitrary precision at arbitrarily low cost, which constitutes a fundamental difference between processesdriven by a fixed thermodynamic force and those driven periodically.
Abstract: Biomolecular networks capable of counting time can be thought of as ``Brownian clocks.'' The energy budgets necessary to run two classes of such clocks, assuming some minimal required precision, are theoretically determined.
126 citations
TL;DR: In this paper, the authors apply the thermodynamic uncertainty relation to a general model of a molecular motor running against an external force or torque, and show that the Stokes efficiency of such motors is universally bounded.
Abstract: The thermodynamic uncertainty relation provides an inequality relating any mean current, the associated dispersion and the entropy production rate for arbitrary non-equilibrium steady states. Applying it here to a general model of a molecular motor running against an external force or torque, we show that the thermodynamic efficiency of such motors is universally bounded by an expression involving only experimentally accessible quantities. For motors pulling cargo through a viscous fluid, a universal bound for the corresponding Stokes efficiency follows as a variant. A similar result holds if mechanical force is used to synthesize molecules of high chemical potential. Crucially, no knowledge of the detailed underlying mechano-chemical mechanism is required for applying these bounds.
123 citations
TL;DR: It is shown that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian, which implies universal bounds on efficiency and power of quantum heat engines.
Abstract: The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
114 citations
TL;DR: In this article, the authors derive the first and second law for resetting processes far from equilibrium and derive a bound on the amount of work required to maintain a resetting process.
Abstract: Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for resetting processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell demon scenario where heat is extracted from a bath at constant temperature.
100 citations
TL;DR: The thermodynamic uncertainty relation is applied to a general model of a molecular motor running against an external force or torque and it is shown that the thermodynamic efficiency of such motors is universally bounded by an expression involving only experimentally accessible quantities.
Abstract: The thermodynamic uncertainty relation provides an inequality relating any mean current, the associated dispersion and the entropy production rate for arbitrary non-equilibrium steady states. Applying it here to a general model of a molecular motor running against an external force or torque, we show that the thermodynamic efficiency of such motors is universally bounded by an expression involving only experimentally accessible quantities. For motors pulling cargo through a viscous fluid, a universal bound for the corresponding Stokes efficiency follows as a variant. A similar result holds if mechanical force is used to synthesize molecules of high chemical potential. Crucially, no knowledge of the detailed underlying mechano-chemical mechanism is required for applying these bounds.
78 citations
TL;DR: A general trade-off between sensory capacity and efficiency is demonstrated: if the sensory capacity is equal to its maximum 1, then the efficiency must be less than 1/2.
Abstract: For a general sensory system following an external stochastic signal, we introduce the sensory capacity. This quantity characterizes the performance of a sensor: sensory capacity is maximal if the instantaneous state of the sensor has as much information about a signal as the whole time series of the sensor. We show that adding a memory to the sensor increases the sensory capacity. This increase quantifies the improvement of the sensor with the addition of the memory. Our results are obtained with the framework of stochastic thermodynamics of bipartite systems, which allows for the definition of an efficiency that relates the rate with which the sensor learns about the signal with the energy dissipated by the sensor, which is given by the thermodynamic entropy production. We demonstrate a general trade-off between sensory capacity and efficiency: if the sensory capacity is equal to its maximum 1, then the efficiency must be less than 1/2. As a physical realization of a sensor we consider a two-component cellular network estimating a fluctuating external ligand concentration as signal. This model leads to coupled linear Langevin equations that allow us to obtain explicit analytical results.
70 citations
TL;DR: It is shown that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency.
Abstract: We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows us to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.
69 citations
TL;DR: In this article, the authors derived the first and second law for reset processes far from equilibrium and derived a bound on the amount of work required to maintain a resetting process using Landauer's principle.
Abstract: Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for reset processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell's demon scenario where heat is extracted from a bath at constant temperature.
68 citations
TL;DR: In this article, it was shown that a clock driven by a periodic variation of an external protocol can achieve arbitrary precision at arbitrarily low cost, and that the uncertainty of the clock can be deduced from the calculable dispersion of a corresponding current.
Abstract: Brownian clocks are biomolecular networks that can count time A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system Typically, such a cycle requires free energy often provided by ATP hydrolysis We investigate the relation between the precision of such a clock and its thermodynamic costs For clocks driven by a constant thermodynamic force, a given precision requires a minimal cost that diverges as the uncertainty of the clock vanishes In marked contrast, we show that a clock driven by a periodic variation of an external protocol can achieve arbitrary precision at arbitrarily low cost This result constitutes a fundamental difference between processes driven by a fixed thermodynamic force and those driven periodically As a main technical tool, we map a periodically driven system with a deterministic protocol to one subject to an external protocol that changes in stochastic time intervals, which simplifies calculations significantly In the non-equilibrium steady state of the resulting bipartite Markov process, the uncertainty of the clock can be deduced from the calculable dispersion of a corresponding current
TL;DR: In this paper, the authors provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes, which is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current.
Abstract: We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system into a non-equilibrium steady state, and the topology of the network. The proof is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current. This formalism allows for a refinement of the bound for systems in equilibrium or with locally vanishing affinities.
TL;DR: For dipolar Janus particles in two-and three-dimensions interacting with a field, the authors predict a novel symmetry akin to, but different from, the one related to entropy production.
Abstract: In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and identify its universal properties using large deviation theory. The limits of slow and fast internal dynamics give rise to a kink-like and parabolic behavior of the corresponding rate functions, respectively. For dipolar Janus particles in two- and three-dimensions interacting with a field, we predict a novel symmetry akin to, but different from, the one related to entropy production. Measurements of these extreme fluctuations could thus be used to infer properties of the underlying, often hidden, network of states.
TL;DR: For dipolar Janus particles in two and three dimensions interacting with a field, the authors predict a novel symmetry akin to, but different from, the one related to entropy production.
Abstract: In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and identify its universal properties using large deviation theory. The limits of slow and fast internal dynamics give rise to a kink-like and parabolic behavior of the corresponding rate functions, respectively. For dipolar Janus particles in two and three dimensions interacting with a field, we predict a novel symmetry akin to, but different from, the one related to entropy production. Measurements of these extreme fluctuations could thus be used to infer properties of the underlying, often hidden, network of states.
TL;DR: This work analyzes the feedback process for the paradigmatic case of a nonequilibrium steady state generated by a dichotomous force protocol, first theoretically for a colloidal particle in a harmonic trap and then with both simulations and experiments for a long DNA hairpin.
Abstract: Controlling a time-dependent force applied to single molecules or colloidal particles is crucial for many types of experiments. Since in optical tweezers the primary controlled variable is the position of the trap, imposing a target force requires an active feedback process. We analyze this feedback process for the paradigmatic case of a nonequilibrium steady state generated by a dichotomous force protocol, first theoretically for a colloidal particle in a harmonic trap and then with both simulations and experiments for a long DNA hairpin. For the first setup, we find there is an optimal feedback gain separating monotonic from oscillatory response, whereas a too strong feedback leads to an instability. For the DNA molecule, reaching the target force requires substantial feedback gain since weak feedback cannot overcome the tendency to relax towards the equilibrium force.
TL;DR: A concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories is derived by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics.
Abstract: We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.
TL;DR: The focus on stochastic thermodynamics as mentioned in this paper is a collection of thirty papers that explore conceptual issues within and around thermodynamics, use this framework for the theoretical modeling and experimental investigation of specific systems, and provide further perspectives on and for this active field.
Abstract: We introduce the thirty papers collected in this 'focus on' issue. The contributions explore conceptual issues within and around stochastic thermodynamics, use this framework for the theoretical modeling and experimental investigation of specific systems, and provide further perspectives on and for this active field.
TL;DR: In this article, the authors provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes, which is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current.
Abstract: We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system into a non-equilibrium steady state, and the topology of the network. The proof is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current. This formalism allows for a refinement of the bound for systems in equilibrium or with locally vanishing affinities.
TL;DR: This work probes the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles bound to a substrate by a weak potential arising from generic interactions, and explores the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.
Abstract: We probe the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles (GUVs) bound to a substrate by a weak potential arising from generic interactions. The substrate is either homogeneous, with GUVs bound only by the weak potential, or is chemically functionalized with a micro-pattern of very strong specific binders. In both cases, the weakly adhered membrane is seen to be confined at a well-defined distance above the surface while it continues to fluctuate strongly. We quantify the fluctuations of the weakly confined membrane at the substrate proximal surface as well as of the free membrane at the distal surface of the same GUV. This strategy enables us to probe in detail the damping of fluctuations in the presence of the substrate, and to independently measure the membrane tension and the strength of the generic interaction potential. Measurements were done using two complementary techniques – dynamic optical displacement spectroscopy (DODS, resolution: 20 nm, 10 μs), and dual wavelength reflection interference contrast microscopy (DW-RICM, resolution: 4 nm, 50 ms). After accounting for the spatio-temporal resolution of the techniques, an excellent agreement between the two measurements was obtained. For both weakly confined systems we explore in detail the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.
TL;DR: This work derives a condition related to the local detailed balance relation that determines whether or not a loss of information occurs if the free-energy difference arising from the signal is symmetrically distributed among the forward and backward rates.
Abstract: We study the information loss of a class of inference strategies that is solely based on time averaging For an array of independent binary sensors (eg, receptors, single electron transistors) measuring a weak random signal (eg, ligand concentration, gate voltage) this information loss is up to 05 bit per measurement irrespective of the number of sensors We derive a condition related to the local detailed balance relation that determines whether or not such a loss of information occurs Specifically, if the free-energy difference arising from the signal is symmetrically distributed among the forward and backward rates, time integration mechanisms will capture the full information about the signal As an implication, for the linear noise approximation, we can identify the same loss of information, arising from its inherent simplification of the dynamics
TL;DR: This work demonstrates discontinuous force thinning due to the driven motion of an external probe in a host medium in an ideal structureless medium and a dilute bath of interacting repulsive particles.
Abstract: Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the driven motion of an external probe in a host medium. We consider two cases: an ideal structureless medium (modeling ultrasoft materials such as polymer melts) and a dilute bath of interacting repulsive particles. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between a large probe and a sufficiently dense host medium.
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TL;DR: In this paper, the authors derive a concise and universal expression of the energy dissipation rate using nonlinear-dynamics quantities characterizing synchronization, and elucidate how synchronization/desynchronization between the oscillators affects it.
Abstract: We formulate the energetics of synchronization in coupled oscillators by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. We derive a concise and universal expression of the energy dissipation rate using nonlinear-dynamics quantities characterizing synchronization, and elucidate how synchronization/desynchronization between the oscillators affects it. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that may be interpreted as the simplest model of synchronization of coupled oscillators in a biophysical system, revealing that the oscillators gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.