Universität Stuttgart

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Subject: search.filters.subject.530Institute: search.filters.UBSInstitut.Institut für Theoretische Physik IIStart date: 2010

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Now showing 1 - 10 of 33
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    Towards an underdamped thermodynamic uncertainty relation
    (2020) Fischer, Lukas P.; Seifert, Udo (Prof. Dr.)
    A recent result of stochastic thermodynamics is the so-called thermodynamic uncertainty relation (TUR). This relation, appearing in the form of an inequality, bounds the precision of fluctuating currents by the entropic costs that are required to drive the non-vanishing mean of the observable. As a consequence, the relation enables the access to parameters that are not accessible in an experimental setting via the precision of a experimentally accessible observable. For instance, it was possible to bound the efficiency of molecular machines by means of their measurable moments of motion. Albeit being generalized and modified to more general terms and dynamics, the putative generalization of the thermodynamic uncertainty relation to underdamped dynamics where the inertia is not negligible remains a puzzling problem. Although there are convincing indications for the overdamped TUR being valid for underdamped dynamics as well in some systems, a straightforward application can also lead to violations of the bound. This thesis summarizes the efforts towards an underdamped generalization of the thermodynamic uncertainty relation and shows challenges and chances that come along by generalization of the TUR. To this end, the intriguing limitations of the TUR in the underdamped domain are explored and discussed. For instance, the TUR is inherently broken for finite times where the evolution is governed by ballistic dynamics due to the inertia being present. Furthermore, it is possible to improve the precision beyond the overdamped bound in presence of velocity dependent forces such as the Lorentz force induced by a magnetic field. Beyond the limitations of the TUR in the underdamped regime, this thesis gives a thorough analysis of the proof that leads to the TUR in the overdamped regime and discusses the obstacles which have to be overcome to find the sought-after proof that is valid for underdamped dynamics. The method is illustrated by deriving thermodynamic bounds that are, however, not as transparent and often not as tight as the original TUR. Finally, a conjecture for a generalized TUR is presented which is based on the precision of free diffusion and holds for all times. The corresponding bound converges to the overdamped TUR in the appropriate limit and tightly bounds the precision, even in the ballistic regime. Being based on free diffusion this conjecture also puts the interpretation of the original TUR in a different perspective.
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    Numerical study of the thermodynamic uncertainty relation for the KPZ-equation
    (2021) Niggemann, Oliver; Seifert, Udo
    A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with the (1+1) dimensional Kardar-Parisi-Zhang equation. In the present paper, the analytical results obtained there in the weak coupling limit are tested via a direct numerical simulation of the KPZ equation with good agreement. The accuracy of the numerical results varies with the respective choice of discretization of the KPZ non-linearity. Whereas the numerical simulations strongly support the analytical predictions, an inherent limitation to the accuracy of the approximation to the total entropy production is found. In an analytical treatment of a generalized discretization of the KPZ non-linearity, the origin of this limitation is explained and shown to be an intrinsic property of the employed discretization scheme.
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    The two scaling regimes of the thermodynamic uncertainty relation for the KPZ-equation
    (2021) Niggemann, Oliver; Seifert, Udo
    We investigate the thermodynamic uncertainty relation for the (1+1) dimensional Kardar-Parisi-Zhang (KPZ) equation on a finite spatial interval. In particular, we extend the results for small coupling strengths obtained previously to large values of the coupling parameter. It will be shown that, due to the scaling behavior of the KPZ equation, the thermodynamic uncertainty relation (TUR) product displays two distinct regimes which are separated by a critical value of an effective coupling parameter. The asymptotic behavior below and above the critical threshold is explored analytically. For small coupling, we determine this product perturbatively including the fourth order; for strong coupling we employ a dynamical renormalization group approach. Whereas the TUR product approaches a value of 5 in the weak coupling limit, it asymptotically displays a linear increase with the coupling parameter for strong couplings. The analytical results are then compared to direct numerical simulations of the KPZ equation showing convincing agreement.
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    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.
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    Nonequilibrium sensing and its analogy to kinetic proofreading
    (2015) Hartich, David; Barato, Andre C.; Seifert, Udo
    For 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.
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    Field-theoretic thermodynamic uncertainty relation : general formulation exemplified with the Kardar-Parisi-Zhang equation
    (2020) Niggemann, Oliver; Seifert, Udo
    We propose a field-theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a Markovian dynamics on a discrete set of states and for overdamped Langevin equations. We first formulate a framework which describes quantities like current, entropy production and diffusivity in the case of a generic field theory. We will then apply this general setting to the one-dimensional Kardar-Parisi-Zhang equation, a paradigmatic example of a non-linear field-theoretic Langevin equation. In particular, we will treat the dimensionless Kardar-Parisi-Zhang equation with an effective coupling parameter measuring the strength of the non-linearity. It will be shown that a field-theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant. The calculations show that the field-theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the Kardar-Parisi-Zhang equation due to an excess term stemming from its non-linearity.
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    Nonlinear phenomena in stochastic thermodynamics : from optimal protocols to criticality
    (2024) Remlein, Benedikt; Seifert, Udo (Prof. Dr.)
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    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.