Universität Stuttgart
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Item Open Access Die Bedeutung der Kontrolle über mikroskopische Freiheitsgrade für die Effizienz optimierter Maschinen(2017) Bauer, Michael; Seifert, Udo (Prof. Dr.)Item Open Access Nonequilibrium dynamics of DNA unfolding(2015) Dieterich, Eckhard; Seifert, Udo (Prof. Dr.)In this thesis, the unfolding of DNA is used as a paradigm to address two topics in the field of the nonequilibrium thermodynamics of small systems. In the first project, a variety of systems is driven into a nonequilibrium steady state (NESS) to investigate whether these systems equilibrate with an effective temperature (see Chapter 4). The systems considered range from a colloidal particle in an optical trap to two-state and multiple-state DNA hairpins. For all systems, both experimental and theoretical results are available. The second project focuses on the feedback mechanism for the applied force in the DNA unfolding setup (see Chapter 5). Both experimental data and simulations are used to study the feedback-controlled dynamics, thus determining the set of feedback parameters for which the control of the force is optimized.Item Open Access Active, phoretic motion(2012) Sabaß, Benedikt C.; Seifert, Udo (Prof. Dr.)This work is dedicated to different aspects of the motion of micro- and nanoparticles that are driven by interaction with a concentration gradient. The swimming of particles in a solution is called diffusiophoresis if it results from the interaction with nonionic solvent gradients. Motion driven by ionic concentration gradients is called electrophoresis or chemiphoresis, depending on whether or not an electric field moves the particle. Recently, the concept of active phoresis has emerged. The new idea is here that the swimming particle produces the concentration gradient by itself. In corresponding experiments the particle mostly catalyzes a chemical reaction in an asymmetric way on its surface. Various realizations of such systems have been explored experimentally during the last years. These swimmers are a unique model system for the investigation of microscale non-equilibrium phenomena. The aim of the thesis is to contribute to an improved understanding of active, phoretic motion. In particular energetic aspects of this type of swimming are investigated for the first time.Item Open Access Thermodynamic bounds on current fluctuations(2018) Pietzonka, Patrick; Seifert, Udo (Prof. Dr.)Living systems, as well as useful artificial machines, operate under non-equilibrium conditions. This means that they are in contact with several reservoirs that are not in mutual thermodynamic equilibrium. These reservoirs provide resources such as food or fuel, or act as a thermal environment absorbing heat. Provided that the system under consideration is sufficiently small compared to the reservoirs, the state of the reservoirs will change negligibly on relevant time scales. If additionally the system is not manipulated externally, its dynamics becomes time-invariant, which is called a non-equilibrium steady state (NESS). Due to the thermal influence from its environment, the state of the system becomes erratic, which allows us to model its dynamics as a stochastic process, for which one can define several thermodynamic observables. Of particular interest throughout this Thesis are the input- and output-currents associated with a NESS. Examples for such currents include the consumption or production of a specific chemical species or the work associated with lifting a weight. A current of particular thermodynamic importance is the production of entropy in the total system, which quantifies its non-equilibrium character. In stark contrast to equilibrium systems, non-equilibrium systems are capable of maintaining non-zero average currents. In particular, the rate of entropy production is, due to the second law of thermodynamics, always greater than zero on average. However, again due to the thermal influence from the environment, the temporal evolution of these currents is superimposed by fluctuations. This means, that on short time scales, currents can deviate from the average intensity, and the entropy production can even become negative. The main objective of the work documented in this Thesis is to provide a comprehensive characterization of the statistics of current fluctuations. While an exact calculation of these statistical properties is possible, the results typically depend on all microscopic details of the system and on the driving forces associated with the reservoirs. Since such detailed information is practically neither available nor relevant, we focus on the derivation of bounds on the statistics of current fluctuations, which ideally depend on only a few thermodynamic properties of the system. Starting point for our work is a prominent inequality known as the “thermodynamic uncertainty relation” [A.C. Barato and U. Seifert, Phys. Rev. Lett. 114, 158101 (2015)]. It considers the uncertainty of a current, comparing the amplitude of its fluctuations to its mean, as a statistical measure and on the other hand the average rate of entropy production as a thermodynamic measure. The product of these two key quantities must always be greater than two, expressing a trade-off between precision and the thermodynamic cost for a non-equilibrium process. It holds for any current and for the huge class of systems that can be described in terms of Markov processes. We put this relation in a wider mathematical context, employing large deviation theory to derive it as a result of an equally general bound on the whole spectrum of current fluctuations. Our formalism allows for several refinements and generalizations of that bound and yields complementary, novel bounds on current fluctuations.Item Open Access Nonequilibrium dynamics of colloids(2013) Lander, Boris; Seifert, Udo (Prof. Dr.)This thesis is dedicated to the nonequilibrium dynamics of colloidal systems. Colloids belong to the class of mesoscopic systems at typical length scales ranging from a few nanometers to several micrometers. In addition to colloids, such systems span proteins, molecular motors, up to living organisms such as bacteria. The mesoscopic regime is mainly characterized by two important properties. First, the small length scale typically entails an accordingly small energy scale in the order of the thermal energy. Hence, thermal fluctuations play a prominent role. Second, mesoscopic systems, especially biological ones, occur mostly under far-from-equilibrium conditions. Stochastic thermodynamics eliminates these problems by extending thermodynamic concepts such as work, heat, and entropy to the level of fluctuating trajectories under fairly general nonequilibrium conditions. The cornerstones of this approach, which has been developed over the past decades, are the first law along fluctuating trajectories and the definition of a stochastic entropy. A central quality of this framework is that it merely requires the coupling to an equilibrated heat bath, while the mesoscopic system itself can be situated arbitrarily far from equilibrium. The goal of this thesis is to investigate different aspects of the nonequilibrium dynamics of colloids in the light of this framework. In order to tackle this task, colloidal systems are ideally suited as their complexity can be varied from simple systems comprising only few degrees of freedom up to interacting many-body systems. In order to address the more fundamental questions in this thesis, we start by considering two interacting colloidal particles driven along two separate rings by optical tweezers. We use this experimentally well-controllable system to introduce and test an efficient method to measure the dissipation rate in nonequilibrium steady states and to investigate how a hidden degree of freedom affects the fluctuation theorem for entropy production. In order to study collective phenomena, we employ a colloidal suspension subject to a linear shear flow. For this system, we examine the fluctuation-dissipation theorem and the closely related Einstein relation in connection with an approximate effective temperature. Moreover, we study the effect of a linear shear flow on the dynamics of the crystallization process if the colloidal suspension is prepared in a supersaturated state.Item Open Access Stochastic thermodynamics of learning(2018) Goldt, Sebastian; Seifert, Udo (Prof. Dr.)Unravelling the physical limits of information processing is an important goal of non-equilibrium statistical physics. It is motivated by the search for fundamental limits of computation, such as Landauer's bound on the minimal work required to erase one bit of information. Further inspiration comes from biology, where we would like to understand what makes single cells or the human brain so (energy-)efficient at processing information. In this thesis, we analyse the thermodynamic efficiency of learning in neural networks. We first discuss the interplay of information processing and dissipation from the perspective of stochastic thermodynamics, a powerful framework to analyse the thermodynamics of strongly fluctuating systems far from equilibrium. We then show that the dissipation of any physical system, in particular a neural network, bounds the information that the network can infer from data or learn from a teacher. Along the way, we illustrate our thermodynamic bounds by looking at a number of examples and we outline directions for future research.Item Open Access Stochastic thermodynamics of information processing: bipartite systems with feedback, signal inference and information storage(2017) Hartich, David; Seifert, Udo (Prof. Dr.)Stochastic thermodynamics is a theoretical framework that extends the laws of classical thermodynamics to small system at the molecular and cellular scale. In particular processing information at theses scales is continuously corrupted by thermal fluctuations. Examples involve translating information from DNA to proteins, bacteria that sense their environment or neurons that fire action potentials. In all of these examples, energy is consumed to process information or to shield the process against thermal fluctuations. This thesis investigates the relation between information and thermodynamics in physical systems. We develop a framework for two continuously coupled systems, which is called stochastic thermodynamics of bipartite systems. This framework includes information and refines the standard second law of thermodynamics. In the first part we consider feedback-driven engines, where one subsystem is controlled by a second subsystem that constitutes the feedback controller. The feedback controller continuously acquires information about the controlled subsystem and uses it to rectify thermal fluctuations, i.e., to "convert information into energy". We compare two information theoretic quantities that characterize the performance of the feedback controller the transfer entropy rate and the learning rate. We find that only the latter both (i) bounds the rate of energy extraction from the medium due to the controlled subsystem and (ii) is itself bounded by the thermodynamic cost to maintain the dynamics of the feedback controller. This insight is one of the main results and provides a modern view on classical thought experiments first proposed by Maxwell. In the second part, we discuss implications to cellular information processing, whereby a stochastic time dependent signal is measured by a sensory network. In contrast to feedback-driven engines, here a sensor dissipates energy to acquire information about a signal, i.e., "it converts energy into information". We define an efficiency that relates the information which a sensor acquires to the energy which is dissipated by the sensor. Models that are inspired by the sensory system of Escherichia coli chemotaxis are used to illustrate our findings. Moreover, a purely information theoretic quantity, which is called sensory capacity, is introduced. The sensory capacity is bounded by one and given by the ratio of the learning rate of the sensor and the transfer entropy rate from the signal to the sensor. The sensory capacity is maximal if the instantaneous state of the sensor knows as much about the signal as its full time history. We show that the sensory capacity can be increased with an additional dissipative memory, where the increase of the sensory capacity characterizes the performance of the memory. A general tradeoff between the sensory capacity and the efficiency is shown, which demonstrates that a sensor cannot be both: a perfect noise filter and energetically efficient. The third subject considers binary sensors (e.g., receptors) measuring a stochastic signal (e.g., ligand concentration). For this setup we study the information loss of inference strategies that are solely based on time-averages of the sensor state. We show that simple time-averaging strategies lose up to 0.5 bit of information compared with the full time history of the sensor. This result holds for an arbitrary number of sensors measuring the same signal independently. Furthermore, we show that the same information loss occurs if one approximates a discrete chemical master equation by a continuous Brownian motion. In the last part, we discuss nonequilibrium receptors that are driven out of equilibrium by an ATP hydrolysis reaction. It is shown that the sensitivity of the receptor to concentration changes can be increased with the nonequilibrium reaction, whereby the increase in sensitivity is related to the chemical energy released in the hydrolysis of one ATP molecule. It turns out that there is an analogy between nonequilibrium receptors and kinetic proofreading, which is a dissipative mechanism to reduce errors in a polymerization process. This part demonstrates that investing chemical energy can improve the capability to process information.Item Open Access Universal bounds on efficiency and power of heat engines with broken time-reversal symmetry(2015) Brandner, Kay; Seifert, Udo (Prof. Dr.)Ever since James Watt's steam engine, the urge to explore the fundamental principles governing the performance of devices that convert thermal energy into useful work was one of the major quests in thermodynamics. From a conceptual point of view, such heat engines can be divided into two classes. Cyclic engines use a reciprocating piston to generate mechanical work by periodically compressing and expanding a working fluid at varying temperature. Thermoelectric engines consist of two heat and particle reservoirs, which are permanently coupled by a conductor. Due to the Seebeck effect, the heat current flowing naturally in this setup can drive a particle current into the same direction thus generating electrical power. Over the last decades, substantial efforts have gone into the miniaturization of both types of devices down to micro- and nanometers. On theses small scales, their operation principles can be scrutinized under the microscope by virtue of precise measurements of characteristic quantities like applied work or exchanged heat. In this thesis, we use the framework of stochastic thermodynamics to investigate the laws that determine the efficiency and power of mesoscopic heat engines in the linear response regime. By using primarily algebraic methods, we obtain three major results. First, we show for the paradigmatic class of multi-terminal thermoelectric heat engines that current conservation implies stronger bounds on the efficiency than the bare second law. These bounds become successively weaker as the number of involved terminals increases. Second, we prove a universal bound on the power of multi-terminal engines, which is a quadratic function of their efficiency and does not depend on model-specific parameters like the number of terminals. In particular, this result rules out the option of Carnot efficiency at finite power, which the laws of thermodynamics would, in principle, allow as Benenti et al. recently pointed out [Phys. Rev. Lett. 106, 230602 (2011)]. Finally, after developing a universal framework for the thermodynamic description of periodically driven systems, as our third main result, we show that the same efficiency-dependent bound on power holds for cyclic micro- and nano heat engines, which obey a Fokker-Planck-type dynamics. Our results constitute a significant step towards a better understanding of heat to work conversion on small scales and reveal an intriguing similarity between cyclic and thermoelectric heat engines. Whether this analogy suggests the existence of a so-far-undiscovered universal principle that applies to both types of devices and leads to a bound on power for any heat engine operating in linear response remains an exciting topic for future research.Item Open Access Vesicles in flow : role of thermal fluctuations(2014) Abreu, David; Seifert, Udo (Prof. Dr.)The present thesis deals with the dynamics of fluid vesicles in flow, with a particular focus on the role of thermal fluctuations. Vesicles are microscopic “bags” of liquid whose membrane consists of a very thin lipid bilayer. They are used in biological systems for intra- and inter-cellular communication. They also serve as pharmaceutical carriers. Moreover, they represent the simplest model system for more complex cells possessing a lipid membrane such as red blood cells. Therefore, studying the dynamics of vesicles in flow has a great biological and technological relevance. We are interested in so-called giant unilamellar vesicles (GUVs). Their size is of the order of 10 micrometers which is much larger than the thickness of their bilayer membrane (5 nanometers). A GUV can thus be modeled as a two-dimensional membrane enclosing a fluid and suspended in another fluid. The membrane is in a liquid phase at room temperature and is to very good approximation incompressible and impermeable to many ions, such that the volume and the surface area of a vesicle remain constant. The bending deformations of the membrane involve much lower energies than the stretching and shearing ones. They are therefore sufficient to predict the equilibrium shapes of vesicles under the two constraints mentioned above. Moreover, the membrane bending energy is around 10 to 50 kT, where kT is the typical thermal energy. Therefore, thermal fluctuations play an important role in the shape transitions of GUVs. In this work, we provide a theoretical analysis of the dynamics of GUVs in planar linear flows consisting of a rotational and an elongational component. Our main goal is to investigate the impact of thermal fluctuations on the different dynamical regimes. In order to derive analytical equations of motion, we consider either undeformable vesicles of ellipsoidal shape, or quasi-spherical vesicles corresponding to slightly deflated spheres. We solve these equations either analytically or numerically. We then compare our theoretical predictions to experiments to elucidate the various phenomena observed therein.Item Open Access Dynamics and thermodynamics of molecular motor-cargo systems(2015) Zimmermann, Eva; Seifert, Udo (Prof. Dr.)This thesis is dedicated to the dynamics and thermodynamics of molecular motors. In particular, it focuses on the influence of a coupled probe particle on the properties of the motor protein. Molecular motors are enzymes that are able to convert chemical energy available from, e.g., ATP hydrolysis into mechanical motion. They are involved in a variety of important processes that account for cellular function like transport of organelles, cell division, muscle contraction and even ATP synthesis. Although molecular motors are microscopic objects of the size of several nanometers whose dynamics is strongly influenced by thermal fluctuations, they exhibit a surprisingly stable and efficient performance. Hence, understanding the structure and mode of operation is of great scientific relevance in the fields of physics, biology, chemistry and medicine. Experimental studies typically imply some kind of probe particle that is attached to the motor and serves as a sensor to visualize the motor motion and that allows to exert forces on the motor under investigation. Since these probe particles are often more than ten times larger than the motor itself, they can be expected to constitute a considerable hindrance to the motor and to severely influence its dynamics and thermodynamics. Inferring properties of the motor from experimental data is a delicate task since on the one hand, only the trajectory of the probe is directly accessible, while on the other hand any measurement results apply to the motor-probe complex rather than the motor itself. In the first place, it is often unclear which properties of the motor are influenced by the coupled probe and to what extent. Belonging to the class of mesoscopic biological systems, the dynamics of molecular motors is subject to thermal fluctuations. Furthermore, the motors operate under genuine nonequilibrium conditions. Hence, a theoretical description of these microscopic machines requires the consideration of fluctuations and nonequilibrium conditions, which is provided by the framework of stochastic dynamics and stochastic thermodynamics. In this thesis, we theoretically analyze the dynamics and energetics of a molecular motor coupled to a probe particle with regard to the effects caused by the presence of the probe. Our goal is to determine the influence of the probe particle on several properties of the motor dynamics and energetics and to identify features in the experimental data that are consequences of attaching a probe and do not belong to the motor itself. Furthermore, we provide a thermodynamically consistent procedure to simplify the theoretical description by mapping motor and probe to an effective motor particle. In order to investigate these effects we set up a generic model comprising two degrees of freedom representing motor and probe, respectively, that are coupled via an elastic linker. Results are obtained from Monte Carlo simulations of the system and from numerically solving the Fokker-Planck equation. In some cases, we also apply simplified models that can be solved analytically. We also compare our results to available experimental data.