arXiv subjects

Udo Seifert

Publications and source records attributed to Udo Seifert.

At least 55 records · Page 3Linked to original sources

arXiv2019

Autonomous engines driven by active matter: Energetics and design principles

Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly.

cond-mat.stat-mech↗

arXiv2019

Field-Theoretic Thermodynamic Uncertainty Relation -- General formulation exemplified with the Kardar-Parisi-Zhang equation

We introduce 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 the field-theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant.

cond-mat.stat-mech↗

arXiv2019

Subharmonic oscillations in stochastic systems under periodic driving

Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics due to thermal fluctuations. In contrast to stochastic autonomous systems in a stationary state, for which the number of coherent oscillations is fundamentally bounded by the number of states in the underlying network, we demonstrate that in periodically driven systems, subharmonic oscillations can, in principle, remain coherent forever, even in networks with a small number of states. We also show that, {\sl inter alia}, the thermodynamic cost rises only logarithmically with the number of coherent oscillations in a model calculation and that the possible periods of the persistent subharmonic response grow linearly with the number of states. We argue that our results can be relevant for biochemical oscillations and for stochastic models of time-crystals.

cond-mat.stat-mech↗

arXiv2019

Affinity-dependent bound on the spectrum of stochastic matrices

Affinity has proven to be a useful tool for quantifying the non-equilibrium character of time continuous Markov processes since it serves as a measure for the breaking of time reversal symmetry. It has recently been conjectured that the number of coherent oscillations, which is given by the ratio of imaginary and real part of the first non-trivial eigenvalue of the corresponding master matrix, is constrained by the maximum cycle affinity present in the network. In this paper, we conjecture a bound on the whole spectrum of these master matrices that constrains all eigenvalues in a fashion similar to the well known Perron-Frobenius theorem that is valid for any stochastic matrix. As in other studies that are based on affinity-dependent bounds, the limiting process that saturates the bound is given by the asymmetric random walk. For unicyclic networks, we prove that it is not possible to violate the bound by small perturbation of the asymmetric random walk and provide numerical evidence for its validity in randomly generated networks. The results are extended to multicyclic networks, backed up by numerical evidence provided by networks with randomly constructed topology and transition rates.

cond-mat.stat-mech↗

arXiv2019

Interlinked GTPase cascades provide a motif for both robust switches and oscillators

GTPases regulate a wide range of cellular processes, such as intracellular vesicular transport, signal transduction, and protein translation. These hydrolase enzymes operate as biochemical switches by toggling between an active guanosine triphosphate (GTP)-bound state and an inactive guanosine diphosphate (GDP)-bound state. We compare two network motifs, a single-species switch and an interlinked cascade that consists of two species coupled through positive and negative feedback loops. We find that interlinked cascades are closer to the ideal all-or-none switch and are more robust against fluctuating signals. While the single-species switch can only achieve bistability, interlinked cascades can be converted into oscillators by tuning the cofactor concentrations, which catalyse the activity of the cascade. These regimes can only be achieved with sufficient chemical driving provided by GTP hydrolysis. In this study, we present a thermodynamically consistent model that can achieve bistability and oscillations with the same feedback motif.

physics.bio-ph↗

arXiv2019

Entropy and the second law for driven, or quenched, thermally isolated systems

The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive part of the entropy change does not become negative. However, for any finite system and small driving, the mean entropy change can well be negative. We derive these results using as micro-canonical entropy a variant recently introduced by Swendsen and co-workers called "canonical". This canonical entropy is the one of a canonical ensemble with the corresponding mean energy. As we show by refining the micro-canonical Crooks relation, the same results hold true for the two more conventional choices of micro-canonical entropy given either by the area of a constant energy shell, the Boltzmann entropy, or the volume underneath it, the Gibbs volume entropy. These results are exemplified with quenched $N$-dimensional harmonic oscillators.

cond-mat.stat-mech↗

arXiv2019

Operationally accessible bounds on fluctuations and entropy production in periodically driven systems

For periodically driven systems, we derive a family of inequalities that relate entropy production with experimentally accessible data for the mean, its dependence on driving frequency, and the variance of a large class of observables. With one of these relations, overall entropy production can be bounded by just observing the time spent in a set of states. Among further consequences, the thermodynamic efficiency both of isothermal cyclic engines like molecular motors under a periodic load and of cyclic heat engines can be bounded using experimental data without requiring knowledge of the specific interactions within the system. We illustrate these results for a driven three-level system and for a colloidal Stirling engine.

cond-mat.stat-mech↗

arXiv2019

Statistical mechanics of an elastically pinned membrane: Static profile and correlations

The relation between thermal fluctuations and the mechanical response of a free membrane has been explored in great detail, both theoretically and experimentally. However, understanding this relationship for membranes, locally pinned by proteins, is significantly more challenging. Given that the coupling of the membrane to the cell cytoskeleton, the extracellular matrix and to other internal structures is crucial for the regulation of a number of cellular processes, understanding the role of the pinning is of great interest. In this manuscript we consider a single protein (elastic spring of a finite rest length) pinning a membrane modelled in the Monge gauge. First, we determine the Green$'$s function for the system and complement this approach by the calculation of the mode coupling coefficients for the plane wave expansion, and the orthonormal fluctuation modes, in turn building a set of tools for numerical and analytic studies of a pinned membrane. Furthermore, we explore static correlations of the free and the pinned membrane, as well as the membrane shape, showing that all three are mutually interdependent and have an identical long-range behaviour characterised by the correlation length. Interestingly, the latter displays a non-monotonic behaviour as a function of membrane tension. Importantly, exploiting these relations allows for the experimental determination of the elastic parameters of the pinning. Last but not least, we calculate the interaction potential between two pinning sites and show that, even in the absence of the membrane deformation, the pinnings will be subject to an attractive force due to changes in membrane fluctuations.

physics.bio-ph↗

arXiv2019

Effect of a magnetic field on the thermodynamic uncertainty relation

The thermodynamic uncertainty relation provides a universal lower bound on the product of entropy production and the fluctuations of any current. While proven for Markov dynamics on a discrete set of states and for overdamped Langevin dynamics, its status for underdamped dynamics is still open. We consider a two-dimensional harmonically confined charged particle in a magnetic field under the action of an external torque. We show analytically that, depending on the sign of the magnetic field, the thermodynamic uncertainty relation does not hold for the currents associated with work and heat. A strong magnetic field can effectively localize the particle with concomitant bounded fluctuations and low dissipation. Numerical results for a three-dimensional variant and for further currents suggest that the existence of such a bound depends crucially on the specific current.

cond-mat.stat-mech↗

arXiv2018

A generalization of the thermodynamic uncertainty relation to periodically driven systems

The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to periodically time-dependent systems and, relatedly, to a larger class of inherently time-dependent current observables. In the context of heat engines or molecular machines, our generalization applies not only to the work performed by constant driving forces, but also to the work performed while changing energy levels. The entropic term entering the generalized uncertainty relation is the sum of local rates of entropy production, which are modified by a factor that refers to an effective time-independent probability distribution. The conventional form of the thermodynamic uncertainty relation is recovered for a time-independently driven steady state and, additionally, in the limit of fast driving. We illustrate our results for a simple model of a heat engine with two energy levels.

cond-mat.stat-mech↗

arXiv2018

Force-dependent diffusion coefficient of molecular Brownian ratchets

We study the mean velocity and diffusion constant in three related models of molecular Brownian ratchets. Brownian ratchets can be used to describe translocation of biopolymers like DNA through nanopores in cells in the presence of chaperones on the trans side of the pore. Chaperones can bind to the polymer and prevent it from sliding back through the pore. First, we study a simple model that describes the translocation in terms of an asymmetric random walk. It serves as an introductory example but already captures the main features of a Brownian ratchet. We then provide an analytical expression for the diffusion constant in the classical model of a translocation ratchet that was first proposed by Peskin et al. . This model is based on the assumption that the binding and unbinding of the chaperones is much faster than the diffusion of the DNA strand. To remedy this shortcoming, we propose a modified model that is also applicable if the (un)binding rates are finite. We calculate the force dependent mean velocity and diffusivity for this new model and compare the results to the original one. Our analysis shows that for large pulling forces the predictions of both models can differ strongly even if the (un)binding rates are large in comparison to the diffusion time-scale but still finite. Furthermore, implications of the thermodynamic uncertainty relation on the efficiency of Brownian ratchets are discussed.

cond-mat.stat-mech↗

arXiv2018

Phase transition in thermodynamically consistent biochemical oscillators

Biochemical oscillations are ubiquitous in living organisms. In an autonomous system, not influenced by an external signal, they can only occur out of equilibrium. We show that they emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality. The control parameter is the thermodynamic force, which must be above a certain threshold for the onset of biochemical oscillations. This critical behavior is characterized by the thermodynamic flux associated with the thermodynamic force, its diffusion coefficient, and the stationary distribution of the oscillating chemical species. We discuss metrics for the precision of biochemical oscillations by comparing two observables, the Fano factor associated with the thermodynamic flux and the number of coherent oscillations. Since the Fano factor can be small even when there are no biochemical oscillations, we argue that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillations. Our results are obtained with three thermodynamically consistent versions of known models: the Brusselator, the activator-inhibitor model, and a model for KaiC oscillations.

cond-mat.stat-mech↗

arXiv2018

Statistical mechanics of an elastically pinned membrane: Equilibrium dynamics and power spectrum

In biological settings membranes typically interact locally with other membranes or the extracellular matrix in the exterior, as well as with internal cellular structures such as the cytoskeleton. Characterization of the dynamic properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modelling pinned membranes has been impeded by the complexity of governing equations. Here we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently-attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, where the elasticity of the membrane's attachment to the cytoskeleton could be measured.

physics.bio-ph↗

arXiv2018

Universal trade-off between power, efficiency, and constancy in steady-state heat engines

Heat engines should ideally have large power output, operate close to Carnot efficiency and show constancy, i.e., exhibit only small fluctuations in this output. For steady-state heat engines, driven by a constant temperature difference between the two heat baths, we prove that out of these three requirements only two are compatible. Constancy enters quantitatively the conventional trade-off between power and efficiency. Thus, we rationalize and unify recent suggestions for overcoming this simple trade-off. Our universal bound is illustrated for a paradigmatic model of a quantum dot solar cell and for a Brownian gyrator delivering mechanical work against an external force.

cond-mat.stat-mech↗

arXiv2018

Large Deviation Function for a Driven Underdamped Particle in a Periodic Potential

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.

cond-mat.stat-mech↗

arXiv2018

Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom

The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of freedom that are hidden from the observer, it is not possible to infer the amount of produced entropy exactly. Previous work suggested that a relation similar to the fluctuation theorem may hold at least approximately for such systems if one considers an apparent entropy production. By extending the notion of apparent entropy production to discrete bipartite systems, we investigate which criteria have to be met for such a modified fluctuation theorem to hold in the large deviation limit. We use asymptotic approximations of the large deviation function to show that the probabilities of extreme events of apparent entropy production always obey a modified fluctuation theorem and, moreover, that it is possible to infer otherwise hidden properties. For the paradigmatic case of two coupled colloidal particles on rings the rate function of the apparent entropy production is calculated to illustrate this asymptotic behavior and to show that the modified fluctuation theorem observed experimentally for short observation times does not persist in the long time limit.

cond-mat.stat-mech↗

arXiv2017

Entropy production of active particles and for particles in active baths

Entropy production of an active particle in an external potential is identified through a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise. In the continuum limit, a unique expression follows, comprising a direct contribution from the active process and an indirect contribution from ordinary diffusive motion. From the corresponding Langevin equation, this physical entropy production cannot be inferred through the conventional, yet here ambiguous, comparison of forward and time-reversed trajectories. Generalizations to several interacting active particles and passive particles in a bath of active ones are presented explicitly, further ones are briefly indicated.

cond-mat.stat-mech↗

arXiv2017

Thermodynamic cost of external control

Artificial molecular machines are often driven by the periodic variation of an external parameter. This external control exerts work on the system of which a part can be extracted as output if the system runs against an applied load. Usually, the thermodynamic cost of the process that generates the external control is ignored. Here, we derive a refined second law for such small machines that include this cost, which is, for example, generated by free energy consumption of a chemical reaction that modifies the energy landscape for such a machine. In the limit of irreversible control, this refined second law becomes the standard one. Beyond this ideal limiting case, our analysis shows that due to a new entropic term unexpected regimes can occur: The control work can be smaller than the extracted work and the work required to generate the control can be smaller than this control work. Our general inequalities are illustrated by a paradigmatic three-state system.

cond-mat.stat-mech↗