Browsing by Author "Seifert, Udo (Prof. Dr.)"

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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.
Open Access
Anwendungen für Renewal Prozesse in der stochastischen Thermodynamik : Semi-Markov Prozesse als Konzept und Werkzeug für zustandsbasierte und übergangsbasierte thermodynamische Inferenz
(2025) Ertel, Benjamin; Seifert, Udo (Prof. Dr.)
Open Access
Die Bedeutung der Kontrolle über mikroskopische Freiheitsgrade für die Effizienz optimierter Maschinen
(2017) Bauer, Michael; Seifert, Udo (Prof. Dr.)
Open Access
Bounds on dynamical quantities in stochastic non-equilibrium systems : from dynamical phenomena to thermodynamic inference
(2024) Degünther, Julius; Seifert, Udo (Prof. Dr.)
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.
Open Access
Elastische Kapseln im hydrodynamischen Fluss
(2010) Keßler, Steffen; Seifert, Udo (Prof. Dr.)
In dieser Arbeit werden elastische Kapseln untersucht, die eine wichtige Klasse weicher Objekte darstellen. Eine elastische Kapsel besteht aus einer dünnen geschlossenen Membran, die eine Flüssigkeit umschließt. Zusätzlich zum Widerstand gegen Biegungen und Flächenänderungen besitzt die Membran einer Kapsel im wesentlichen Unterschied zu fluiden Vesikeln eine endliche Scherelastizität. Ziel dieser Arbeit war es, das Verhalten einer einzelnen elastischen Kapsel in linearen hydrodynamischen Flüssen theoretisch zu untersuchen. Die Kapsel besitzt dabei stets eine ellipsoidale Referenzform. Die Kapsel wird in einen äußeren viskosen Fluss eingebettet. Die Viskosität der äußeren Flüssigkeit kann sich von der Viskosität der inneren Flüssigkeit unterscheiden. Ihr Verhältnis definiert den Viskositätskontrast. In allen typischen Experimenten sind die Längenskalen derart klein, dass die Dissipation über die Trägheit dominiert und die Flüsse durch die Stokes-Gleichungen beschrieben werden. Bei einer Kapsel im Fluss handelt es sich aus theoretischer Sicht um ein herausforderndes nicht-lineares Problem, weil Position und Deformation der Membran nicht a priori bekannt sind, sondern sich aus einem Wechselspiel zwischen hydrodynamischen Kräften und elastischen Membrankräften ergeben. Deshalb erfordert das Lösen der vollständigen Bewegungsgleichungen numerische Methoden, während eine analytische Behandlung nur in Grenzfällen möglich ist. Das vollständige Problem lässt sich vereinfachen, indem die Dynamik der Kapsel auf einige wenige relevante Freiheitsgrade eingeschränkt wird. Das Paradebeispiel einer solchen Reduktion findet sich im Keller-Skalak Modell, in dem ein ellipsoidales rotes Blutkörperchen im Scherfluss durch zwei Freiheitsgrade beschrieben werden soll. Die ellipsoidale Membranform wird hier als fest vorausgesetzt. Die Orientierung der Kapsel ist durch den Anstellwinkel gegeben, der den Winkel zwischen langer Halbachse und Scherflussrichtung misst. Als zweiter Freiheitsgrad dient ein Phasenwinkel, der die Panzerkettenbewegung der Membran beschreibt. Aus der Forderung von Energie- und Drehimpulserhaltung folgen die beiden Bewegungsgleichungen für den Anstell- und den Phasenwinkel. Um die elastische Rückstellkraft zu berücksichtigen, wurde das Keller-Skalak Modell zum reduzierten Kapselmodell erweitert. Das Phasendiagramm zeigt drei verschiedene Bereiche, in denen die Kapsel entweder taumelt, schwingt oder eine intermittierende Bewegung ausübt. Im quasisphärischen Grenzfall wird eine vollständige analytische Lösung der Bewegungsgleichungen des reduzierten Modells vorgestellt. Um die Gültigkeit des reduzierten Modells zu überprüfen, werden die vollständigen Bewegungsgleichungen numerisch mit einer speziell entwickelten Spektralmethode integriert. Ein Phasendiagramm konnte für einen großen Bereich der Scherrate und des Viskositätskontrasts bestimmt werden. Qualitativ und was die Größenordnung angeht auch quantitativ bestätigen sich die Ergebnisse des reduzierten Modells innerhalb des Schwing- und des Taumelbereichs. Ein anderes Verhalten ergibt sich jedoch im Intermittenzbereich, wo sich innerhalb der Spektralmethode ein transientes Verhalten zeigt, bei dem die Kapsel von einer anfänglichen Taumelbewegung in eine stabile Schwingbewegung relaxiert. Um das Intermittenzproblem zu lösen, wird in dieser Arbeit ein systematischer störungstheoretischer Zugang gewählt. Für eine quasisphärische Referenzmembran wird der Grenzfall kleiner Deformationen betrachtet, bei dem eine Entwicklung um eine Kugel möglich wird. Die Zahl der Freiheitsgrade reduziert sich auf die beiden Winkel, Anstellwinkel und Phasenwinkel, sowie auf einen Formparameter, der angibt, wie sehr die Kapsel innerhalb der Scherebene gestreckt ist. Numerische Integration der approximativen Bewegungsgleichungen liefert im Schwing– und Taumelbereich ein analoges Phasendiagramm wie beim reduzierten Modell. Im Intermittenzbereich jedoch ergibt sich ein eindeutig transientes Verhalten. Nach einer Relaxation der Form werden die anfänglichen Taumelbewegungen durch stabile Schwingbewegungen abgelöst. Die numerische Phänomenologie kann im Grenzfall starker Flüsse durch analytische Ergebnisse untermauert werden. Das Intermittenzrätsel löst sich zu Gunsten einer transienten Schwingbewegung. Die Dynamik einer ellipsoidalen Kapsel im linearen Fluss wurde durch numerische und analytische Betrachtungen innerhalb dieser Arbeit vollständig bestimmt und verstanden. Die entscheidenden Freiheitsgrade, die sich aus Form und Orientierung der Kapsel sowie der Panzerkettenbewegung ihrer Membran zusammensetzen, konnten samt ihrer gegenseitigen Einflussnahme identifiziert werden.
Open Access
Krümmungsinduzierte Wechselwirkungen zwischen fluktuierenden Membranen und diffundierenden Proteinen
(2010) Leitenberger, Stefan; Seifert, Udo (Prof. Dr.)
In dieser Arbeit wird ein Modell präsentiert, welches den Einfluss von mechanischen und geometrischen Eigenschaften der Proteine auf die Dynamik der Membran und die laterale Diffusion der Proteine beschreibt. Dazu zählen der Radius, eine spontane Krümmung und die Biegesteifigkeit. Die Gesamtenergie des Systems entspricht der Helfrichenergie mit zusätzlichen Korrekturtermen für die eingebetteten Proteine. Aus dieser Energie werden die für die durchgeführten Rechnungen und Simulationen benötigten Bewegungsgleichungen des Systems aus der Gesamtenergie des Systems abgeleitet. Für die Simulationen wird die kontinuierliche Membran auf ein Gitter übertragen. Die Proteindiffusion entlang der Membran ist jedoch nicht auf das Gitter beschränkt, und die Proteine können Positionen zwischen den Gitterpunkten einnehmen. Um die Resultate besser mit Experimenten vergleichen zu können, wird die projizierte Proteindiffusion in eine Beobachtungsebene untersucht. Für die zeitliche Entwicklung des Systems werden diskretisierte Bewegungsgleichungen für die Membrandynamik und die Diffusion verwendet. Diese, durch die Membranhöhe und die Proteinorte gekoppelten Gleichungen, werden abwechselnd schrittweise ausgeführt bis die vorgegebene Anzahl von Zeitschritten erreicht ist. Die veränderte Bewegungsgleichung für die Membrandynamik führt zu veränderten Mittelwerten und Korrelationen für die Membranhöhe. Für die zeitabhängige Höhen-Höhen-Korreltaion werden zwei Zeitregime gefunden, welche den Zeitskalen der Membrandynamik und der Proteindiffusion entsprechen. Über einen Pfadintegralformalismus wird nachfolgend eine Gleichung für die effektive Proteindiffusion abgeleitet. Diese Diffusion ist im Bezug auf die ungestörte freie Diffusion deutlich reduziert. Im Anschluss an diese Betrachtugen wird das System auf zwei eingebettete Proteine erweitert. Dabei tritt eine fluktuations-induzierte Wechselwirkung zwischen den Proteinen auf, welche je nach Vorzeichen der spontanten Krümmung attraktiv oder repulsiv ist. Für dieses neue System werden nun ebenfalls die Höhen-Höhen-Korrelation und die effektive Diffusion untersucht.
Open Access
Modellierung der Adhäsion und Deformation von Mikrokapseln
(2007) Graf, Peter; Seifert, Udo (Prof. Dr.)
Mikrokapseln spielen eine wichtige Rolle beim Einschluß und der kontrollierten Freisetzung von Substanzen sowohl in industriellen Anwendungen als auch in der Medizin und den Biowissenschaften. Sie dienen ebenso als Modellsysteme für biologische Objekte wie Zellen oder Viruskapseln. Bei vielen dieser Anwendungen sind gute Kenntnisse über die mechanischen Eigenschaften nötig. Typischerweise wird die Kapsel zu diesem Zweck verformt und die dazu benötigten Kräfte werden gemessen. Die Deformation kann auf verschiedene Arten hervorgerufen werden, z. B. durch Adhäsion, äußere Kräfte oder Druckunterschiede zwischen der Innen- und Außenseite der Kapsel. In Experimenten wurde der Adhäsionsradius der Kapsel oder die zum Zusammendrücken der Kapsel benötigte Kraft gemessen. In der vorliegenden Dissertation wird die Adhäsion von Mikrokapseln und die Deformation durch äußere Kräfte auf theoretischem Wege untersucht. Es wird mit Mitteln der Elastizitätstheorie ein Modell entwickelt, mit dem sich die Deformation der Kapsel in Abhängigkeit von den angreifenden Kräften beschreiben läßt. In einer systematischen Untersuchung werden die Vorhersagen des Modells mit experimentellen Daten verglichen, um daraus die elastischen Parameter zu extrahieren.
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.
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.
Open Access
Nonlinear phenomena in stochastic thermodynamics : from optimal protocols to criticality
(2024) Remlein, Benedikt; Seifert, Udo (Prof. Dr.)
Open Access
On stochastic thermodynamics under incomplete information : thermodynamic inference from Markovian events
(2024) Meer, Jann van der; Seifert, Udo (Prof. Dr.)
Open Access
Optimal processes in stochastic thermodynamics
(2009) Schmiedl, Tim; Seifert, Udo (Prof. Dr.)
The concept of Stochastic Thermodynamics deals with the question how to define thermodynamic quantities for nonequilibrium mesoscopic systems. Here, thermal fluctuations must be considered. The main objective of this thesis is the analysis of optimization problems in the context of Stochastic Thermodynamcis. A quite natural optimization principle for nonequilibrium processes is the requirement that a defined result should be achieved with the smallest possible amount of dissipation. For a transition between two given equilibrium states in a given finite time, this is directly linked to a process schedule which leads to a minimal (mean) work. For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. Surprisingly, the optimal protocol involves jumps for overdamped Langevin dynamics and even delta-type singularities for underdamped Langevin dynamics. For purely Hamiltonian and Schrödinger dynamics in harmonic potentials, we show that the optimal protocol is highly degenerate and that even in the limit of short transition times, the optimal work is given by the adiabatic work which is substantially smaller than the work for an instantaneous jump. These optimal protocols significantly improve free energy calculations via the Jarzynski equality. Most processes in the biological cell, however, cannot be described by a nonequilibrium transition between equilibrium states. Rather, these systems are permanently driven out of equilibrium, e.g. by chemical potential differences. An important model class of such dynamics are Brownian motors which transfer either chemical or thermal energy into mechanical work leading to directed transport against a load force. It is meaningful to characterize such thermodynamic machines by their performance at maximum power output rather than at maximum efficiency. The efficiency at this maximum power then is a relevant quantity. We consider a Carnot engine on the mesoscale which can be constructed by using a Brownian particle instead of the working gas and a time-dependent trapping potential instead of the confining vessel. The efficiency at maximum power output can be calculated analytically. Surprisingly, it is given by a quite universal expression which does only depend on the viscosity (or more generally on the mobility matrices) at the two temperatures. This result is independent of the shape of the potential used to trap the particle. In contrast to heat engines, molecular motors in the biological cell are mostly driven by chemical potential differences. For two simple motor models, the efficiency of the molecular motor at maximum power shows two unexpected features: (i) Both the power output and the efficiency increase when the transition state position is moved closer to the initial motor position and (ii) for appropriate parameters, the efficiency increases when the system is driven further out of equilibrium by a higher chemical potential difference. Beyond their relevance for directed transport within the cell, molecular motors are also important for the synthesis of proteins. We study the protein production rate at a given error rate for the second stage of gene expression (translation). We find that for a given error rate equivalent to the experimentally observed value, the protein production rate is not at its theoretical maximum. We therefore conjecture that other evolutionary goals or structural reasons are responsible for the observed rate constants.
Open Access
Phase transitions in thermodynamically consistent biochemical systems
(2020) Nguyen, Basile; Seifert, Udo (Prof. Dr.)
Open Access
Stochastic thermodynamics : from hydrodynamics to stochastic inference
(2021) Uhl, Matthias; Seifert, Udo (Prof. Dr.)
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.
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.
Open Access
Stochastische Thermodynamik kohärenter Oszillationen
(2022) Oberreiter, Lukas; Seifert, Udo (Prof. Dr.)
Open Access
Theorie zu kraftmikroskopischen Einzelmolekülexperimenten an Biopolymeren
(2004) Braun, Oliver; Seifert, Udo (Prof. Dr.)
Die räumliche Struktur von Proteinen und ihre Faltungsdynamik in lebenden Zellen wird wesentlich von der zugrundeliegenden Freien Energielandschaft bestimmt. Die systematische Untersuchung dieser Struktur und der Funktion von Biopolymeren ist eines der Gebiete der Biophysik. In den letzten Jahren wurden die dazu notwendigen Kraftmikroskope, wie das Rasterkraftmikroskop, die optische und magnetische Pinzette sowie die Biomembransonde und damit zusammenhängende experimentelle Techniken entscheidend weiterentwickelt. Einzelne Biopolymere können damit mechanisch manipuliert werden, indem Kräfte in der Größenordnung von pN angelegt werden. Die vorliegende Dissertation beschäftigt sich mit der theoretischen Beschreibung solcher kraftmikroskopischer Experimente. Die zentrale Zielsetzung ist die Rekonstruktion der Freien Energielandschaft aus experimentellen Messdaten sowie aus Daten molekulardynamischer Simulationen. Zur Beschreibung der stochastischen Wärmebewegung der molekularen Systeme finden Konzepte der statistischen Physik Verwendung. Die experimentell angelegten zeitabhängigen Kräften lenken das Systeme zudem häufig aus dem thermischen Gleichgewicht aus. Daher benötigt man Hilfsmittel aus der Theorie der Nichtgleichgewichtsprozesse: die Langevin-Gleichung, die Fokker-Planck-Gleichung, die Mastergleichung und die Jarzynski-Gleichung. Für die verschiedenen biomolekularen Systeme, die hierbei untersucht werden, wie z.B. das Muskelprotein Titin, die DNA und Rezeptor-Ligand Systeme, werden verschiedene Modelle entwickelt und angewandt. Eine besonders wichtige Rolle für die Optimierung der Datenausbeute spielt das experimentelle Protokoll und dessen Parameter.
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.