Showing papers by "Udo Seifert published in 2020"
TL;DR: Thermodynamic uncertainty relations derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states and extend these relations beyond currents to state variables and the quality of the bound is discussed for various types of observables.
Abstract: Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states and extend these relations beyond currents to state variables. The quality of the bound is discussed for various types of observables for an interacting pair of colloidal particles in a moving laser trap and for the dynamical unfolding of a small protein. Since the input for evaluating these bounds does not require specific knowledge of the system or its coupling to the time-dependent control, they should become widely applicable tools for thermodynamic inference in time-dependently driven systems.
109 citations
TL;DR: The properties of driven free diffusion in the underdamped regime are analyzed and it is shown that it inherently violates the overdamped TUR for finite times and a bound for one-dimensional driven diffusion in a potential is conjecture based on the result for free diffusion.
Abstract: The putative generalization of the thermodynamic uncertainty relation (TUR) to underdamped dynamics is still an open problem. So far, bounds that have been derived for such a dynamics are not particularly transparent and they do not converge to the known TUR in the overdamped limit. Furthermore, it was found that there are restrictions for a TUR to hold such as the absence of a magnetic field. In this article we first analyze the properties of driven free diffusion in the underdamped regime and show that it inherently violates the overdamped TUR for finite times. Based on numerical evidence, we then conjecture a bound for one-dimensional driven diffusion in a potential which is based on the result for free diffusion. This bound converges to the known overdamped TUR in the corresponding limit. Moreover, the conjectured bound holds for observables that involve higher powers of the velocity as long as the observable is odd under time reversal. Finally, we address the applicability of this bound to underdamped dynamics in higher dimensions.
21 citations
TL;DR: In this article, a field-theoretic thermodynamic uncertainty relation was proposed for the one-dimensional Kardar-parisi-Zhang equation, an extension of the one derived so far for Markovian dynamics on a discrete set of states and for overdamped Langevin equations.
Abstract: 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.
18 citations
TL;DR: In this paper, the authors show that the fluctuations of the entropy production have an exponential volume-dependence when the system is bistable, and they extend this model to any chemical network.
Abstract: In chemical reaction networks, bistability can only occur far from equilibrium. It is associated with a first-order phase transition where the control parameter is the thermodynamic force. At the bistable point, the entropy production is known to be discontinuous with respect to the thermodynamic force. We show that the fluctuations of the entropy production have an exponential volume-dependence when the system is bistable. At the phase transition, the exponential prefactor is the height of the effective potential barrier between the two fixed-points. Our results obtained for Schl\"ogl's model can be extended to any chemical network.
10 citations
TL;DR: In this paper, the authors introduced a simple model for a simple biochemical oscillator, the Brusselator, and quantified the performance using the number of coherent oscillations, showing that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.
Abstract: Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady-state (NESS). In reality, these processes take place in finite systems containing a finite number of molecules. In such systems, a NESS can be reached with the help of an externally driven pump for which we introduce a simple model. The crucial parameters are the pumping rate and the finite size of the chemical reservoir. We apply this model to a simple biochemical oscillator, the Brusselator, and quantify the performance using the number of coherent oscillations. As a surprising result, we find that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.
6 citations
TL;DR: The entropy of a thermally isolated system should not decrease after a quench or external driving for a large system in the sense that the extensive part of the entropy change does not become negative, but for any finite system and small driving, the mean entropy change can well be negative.
Abstract: 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.
4 citations
TL;DR: In this article, the analytical results obtained there in the weak coupling limit are tested via a direct numerical simulation of the Kardar-Parisi-Zhang equation with good agreement, and an inherent limitation to the accuracy of the approximation to the total entropy production is found.
Abstract: 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.
2 citations
TL;DR: A simple model is applied to a simple biochemical oscillator, the Brusselator, and it is found that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.
Abstract: Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady state (NESS). In reality, these processes take place in finite systems containing a finite number of molecules. In such systems, a NESS can be reached with the help of an externally driven pump for which we introduce a simple model. Crucial parameters are the pumping rate and the finite size of the chemical reservoir. We apply this model to a simple biochemical oscillator, the Brusselator, and quantify the performance using the number of coherent oscillations. As a surprising result, we find that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.
2 citations
Posted Content•
TL;DR: It is shown that the fluctuations of the entropy production have an exponential volume-dependence when the system is bistable and the exponential prefactor is the height of the effective potential barrier between the two fixed-points.
Abstract: In chemical reaction networks, bistability can only occur far from equilibrium. It is associated with a first-order phase transition where the control parameter is the thermodynamic force. At the bistable point, the entropy production is known to be discontinuous. We show that the fluctuations of the entropy production have an exponential volume-dependence when the system is bistable. At the phase transition, the exponential prefactor is the height of the effective potential barrier between the two fixed-points. Our results obtained for Schlogl's model can be extended to any chemical network.
2 citations
TL;DR: In this article, an iterative calculation scheme was proposed to obtain the propagator if the potential consists of a finite number of steps, and the method converges after one iteration, thus providing an expression for the propagators in closed form.
Abstract: Although driven Brownian particles are ubiquitous in stochastic dynamics and often serve as paradigmatic model systems for many aspects of stochastic thermodynamics, fully analytically solvable models are few and far between. In this paper, we introduce an iterative calculation scheme, similar to the method of images in electrostatics, that enables one to obtain the propagator if the potential consists of a finite number of steps. For the special case of a single potential step, this method converges after one iteration, thus providing an expression for the propagator in closed form. In all other cases, the iteration results in an approximation that holds for times smaller than some characteristic timescale that depends on the number of iterations performed. This method can also be applied to a related class of systems like Brownian ratchets, which do not formally contain step potentials in their definition, but impose the same kind of boundary conditions that are caused by potential steps.
1 citations