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 Nonequilibrium sensing and its analogy to kinetic proofreading(2015) Hartich, David; Barato, Andre C.; Seifert, UdoFor a paradigmatic model of chemotaxis, we analyze the effect of how a nonzero affinity driving receptors out of equilibrium affects sensitivity. This affinity arises whenever changes in receptor activity involve adenosine triphosphate hydrolysis. The sensitivity integrated over a ligand concentration range is shown to be enhanced by the affinity, providing a measure of how much energy consumption improves sensing. With this integrated sensitivity we can establish an intriguing analogy between sensing with nonequilibrium receptors and kinetic proofreading: the increase in integrated sensitivity is equivalent to the decrease of the error in kinetic proofreading. The influence of the occupancy of the receptor on the phosphorylation and dephosphorylation reaction rates is shown to be crucial for the relation between integrated sensitivity and affinity. This influence can even lead to a regime where a nonzero affinity decreases the integrated sensitivity, which corresponds to anti-proofreading.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 Thermodynamics of micro- and nano-systems driven by periodic temperature variations(2015) Brandner, Kay; Saito, Keiji; Seifert, UdoItem 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 Functional integral approach to time-dependent heat exchange in open quantum systems : general method and applications(2015) Carrega, M.; Solinas, P.; Braggio, A.; Sassetti, M.; Weiß, UlrichWe establish the path integral approach for the time-dependent heat exchange of an externally driven quantum system coupled to a thermal reservoir. We derive the relevant influence functional and present an exact formal expression for the moment generating functional which carries all statistical properties of the heat exchange process for general linear dissipation. The method is applied to the time-dependent average heat transfer in the dissipative two-state system (TSS). We show that the heat can be written as a convolution integral which involves the population and coherence correlation functions of the TSS and additional correlations due to a polarization of the reservoir. The corresponding expression can be solved in the weak-damping limit both for white noise and for quantum mechanical coloured noise. The implications of pure quantum effects are discussed. Altogether a complete description of the dynamics of the average heat transfer ranging from the classical regime down to zero temperature is achieved.