Showing papers by "Udo Seifert published in 2007"
TL;DR: For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time.
Abstract: For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicit solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and at the end of the process.
302 citations
TL;DR: In this article, a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics was studied and it was shown that for infinitely long cycle times, the engine works at the Carnot efficiency limit producing zero power.
Abstract: We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.
279 citations
TL;DR: For chemical reaction networks in a dilute solution described by a master equation, the authors define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stoChastic trajectory of reaction events.
Abstract: For chemical reaction networks in a dilute solution described by a master equation, the authors define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work, and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations such as a generalized Jarzynski relation and a generalized Clausius inequality are discussed. The authors illustrate these results for a three-species cyclic reaction network whi...
172 citations
TL;DR: The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime and a recent theoretical generalization of the Einstein relation to the nonequilibrium regime is tested.
Abstract: The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical generalization of the Einstein relation to the nonequilibrium regime which involves an integral over measurable velocity correlation functions.
153 citations
TL;DR: In this paper, the deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method, where the shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions.
Abstract: The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.
115 citations
TL;DR: For a colloidal particle driven by a constant force across a periodic potential, this article investigated the distribution of entropy production both experimentally and theoretically, showing that the fluctuation theorem holds experimentally.
Abstract: For a colloidal particle driven by a constant force across a periodic potential, we investigate the distribution of entropy production both experimentally and theoretically. For short trajectories, the fluctuation theorem holds experimentally. The mean entropy production rate shows two regimes as a function of the applied force. Theoretically, both mean and variance of the pronounced non-Gaussian distribution can be obtained from a differential equation in good agreement with the experimental data.
83 citations
TL;DR: In this article, the Jarzynski relation for general stochastic processes including non-Markovian systems with memory was shown to be true for all non-ergodic systems.
Abstract: We prove the Jarzynski relation for general stochastic processes including non-Markovian systems with memory. The only requirement for our proof is the existence of a stationary state, therefore excluding non-ergodic systems. We then show how the concepts of stochastic thermodynamics can be used to prove further exact non-equilibrium relations like the Crooks relation and the fluctuation theorem on entropy production for non-Markovian dynamics.
77 citations
TL;DR: In this paper, entropy change along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium entropy, and the total entropy change obeys an integral fluctuation theorem and a class of further exact relations.
Abstract: Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the surrounding medium. Within a Langevin dynamics, a unique identification of these two contributions is possible. The total entropy change obeys an integral fluctuation theorem and a class of further exact relations, which we prove for arbitrarily coupled slow degrees of freedom including hydrodynamic interactions. These theoretical results can therefore also be applied to driven colloidal systems. For transitions between different internal conformations of a biomolecule involving unbalanced chemical reactions, we provide a thermodynamically consistent formulation and identify again the two sources of entropy production, which obey similar exact relations. We clarify the particular role degenerate states have in such a description.
62 citations
TL;DR: For a colloidal particle driven by a constant force across a periodic potential, the authors investigated the distribution of entropy production both experimentally and theoretically, showing that the fluctuation theorem holds experimentally.
Abstract: For a colloidal particle driven by a constant force across a periodic potential, we investigate the distribution of entropy production both experimentally and theoretically. For short trajectories, the fluctuation theorem holds experimentally. The mean entropy production rate shows two regimes as a function of the applied force. Theoretically, both mean and variance of the pronounced non-Gaussian distribution can be obtained from a differential equation in good agreement with the experimental data.
55 citations
TL;DR: A simple theoretical framework is developed that accounts for the equilibrium state of adhesion and successfully merges the macroscopic and microscopic aspects of the problem.
Abstract: We review the specific adhesion between ligand-containing vesicles and receptor-functionalized substrates as an established model system used to study the cell recognition process and its control mechanisms. In order to provide better understanding of the underlying physics and to allow for quantitative exploitation of this system, we develop a simple theoretical framework that accounts for the equilibrium state of adhesion and successfully merges the macroscopic and microscopic aspects of the problem. Several mechanisms that are used to control adhesion or induce de-adhesion are studied on the same level of theory. Specifically, the repelling properties of adhesive molecules, the role of repelling molecules, the action of antagonists for a specific binder as well as the influence of an externally applied force are addressed independently within the same formalism.
53 citations
TL;DR: In this paper, the Jarzynski relation for general stochastic processes including non-Markovian systems with memory was shown to be true for all non-ergodic systems.
Abstract: We prove the Jarzynski relation for general stochastic processes including non-Markovian systems with memory. The only requirement for our proof is the existence of a stationary state, therefore excluding non-ergodic systems. We then show how the concepts of stochastic thermodynamics can be used to prove further exact non-equilibrium relations like the Crooks relation and the fluctuation theorem on entropy production for non-Markovian dynamics.
TL;DR: A method to simulate lateral diffusion of inclusions in a fluctuating membrane using the membrane equation and the Langevin equation for the particle and a detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.
Abstract: In this paper we introduce a method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.
TL;DR: Based on the concept of a nonequilibrium steady state, a method to experimentally determine energy landscapes acting on colloidal systems by measuring the stationary probability distribution and the current in the system is presented.
Abstract: Based on the concept of a nonequilibrium steady state, we present a method to experimentally determine energy landscapes acting on colloidal systems. By measuring the stationary probability distribution and the current in the system, we explore potential landscapes with barriers up to several hundred ${k}_{\mathrm{B}}T$. As an illustration, we use this approach to measure the effective diffusion coefficient of a colloidal particle moving in a tilted potential.
TL;DR: In this study, the lateral diffusion of a protein interacting with the curvature of the membrane is considered and it is found that this curvature coupling substantially enhances the diffusion coefficient.
Abstract: We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.
TL;DR: A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules that can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions.
Abstract: A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur et al., Science 264, 945 (1994); M.S. Spector et al., Langmuir 14, 3493 (1998); Y. Zhao, et al., Proc. Natl. Acad. Sci. USA 102, 7438 (2005)] on self-assembled chiral lipid membranes of ${\mathrm{DC}}_{8,9}\mathrm{PC}$. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0\ifmmode^\circ\else\textdegree\fi{} and 35\ifmmode^\circ\else\textdegree\fi{}, which are close to the most frequent values 5\ifmmode^\circ\else\textdegree\fi{} and 28\ifmmode^\circ\else\textdegree\fi{} observed in the experiment [N. Mahajan et al., Langmuir 22, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left- and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda et al., Nature (London) 399, 566 (1999)].
TL;DR: This work compares quasi-analytical results for tethers with analytical results for corresponding continuous models and investigates under what circumstances the discrete nature of the tethers actually influences the fluctuations.
Abstract: Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.
TL;DR: In this article, a first-law like energy balance involving exchanged heat and entropy production entering refinements of the second law can consistently be defined along single stochastic trajectories.
Abstract: Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and entropy production entering refinements of the second law can consistently be defined along single stochastic trajectories. Various exact relations involving the distribution of such quantities like integral and detailed fluctuation theorems for total entropy production and the Jarzynski relation follow from such an approach based on Langevin dynamics. Analogues of these relations can be proven for any system obeying a stochastic master equation like, in particular, (bio)chemically driven enzyms or whole reaction networks. The perspective of investigating such relations for stochastic field equations like the Kardar-Parisi-Zhang equation is sketched as well.