Universität Stuttgart
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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 Thermodynamics of micro- and nano-systems driven by periodic temperature variations(2015) Brandner, Kay; Saito, Keiji; Seifert, UdoItem 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.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 Coherence-enhanced efficiency of feedback-driven quantum engines(2015) Brandner, Kay; Bauer, Michael; Schmid, Michael T.; Seifert, UdoA genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that this additional energetic cost leads to a stronger bound on the work extractable after a single measurement from a system initially in thermal equilibrium (2009 Phys. Rev. A 80 012322). Here, we extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time. The bound thus implies a natural definition for the efficiency of information to work conversion in such devices. For a simple model consisting of a laser-driven two-level system, we maximize the efficiency with respect to the observable whose measurement is used to control the feedback operations. We find that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two level system. This result reveals that periodic feedback engines operating in the quantum realm can exploit quantum coherences to enhance efficiency.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.Item Open Access Multiscale approaches to protein-mediated interactions between membranes : relating microscopic and macroscopic dynamics in radially growing adhesions(2015) Bihr, Timo; Seifert, Udo; Smith, Ana-SunčanaMacromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of deformable membranes, the diffusion of proteins and the molecular binding and unbinding. Because these stochastic processes couple over a multitude of time and length scales, theoretical modeling of membrane adhesion has been a major challenge. Here we present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local rates for molecular recognition. The latter step in the Monte Carlo approach enables us to simulate the nucleation and growth of adhesion domains within a system of the size of a cell for tens of seconds without loss of accuracy, as shown by comparison to 106 times more expensive Langevin simulations. To perform this validation, the Langevin approach was augmented to simulate diffusion of proteins explicitly, together with reaction kinetics and membrane dynamics. We use the Monte Carlo scheme to gain deeper insight to the experimentally observed radial growth of micron sized adhesion domains, and connect the effective rate with which the domain is growing to the underlying microscopic events. We thus demonstrate that our technique yields detailed information about protein transport and complexation in membranes, which is a fundamental step toward understanding even more complex membrane interactions in the cellular context.