Showing papers by "Udo Seifert published in 2021"
TL;DR: This work introduces a thermodynamically consistent model for a discrete time crystal and analyzes it using the framework of stochastic thermodynamics to demonstrate that the emergence of coherent oscillations is possible even in the absence of synchronization.
Abstract: Discrete time crystals are periodically driven systems that display spontaneous symmetry breaking of time translation invariance in the form of indefinite subharmonic oscillations. We introduce a thermodynamically consistent model for a discrete time crystal and analyze it using the framework of stochastic thermodynamics. In particular, we evaluate the rate of energy dissipation of this many-body system of interacting noisy subharmonic oscillators in contact with a heat bath. The mean-field model displays the phenomenon of subharmonic synchronization, which corresponds to collective subharmonic oscillations of the individual units. The 2D model does not display synchronization but it does show a time-crystalline phase, which is characterized by a power-law behavior of the number of coherent subharmonic oscillations with system size. This result demonstrates that the emergence of coherent oscillations is possible even in the absence of synchronization.
11 citations
TL;DR: In this paper, the authors prove that for a system with discrete states, the optimal process involves non-conservative driving, i.e., a genuine driving affinity is bounded by the number of states within each cycle.
Abstract: An optimal finite-time process drives a given initial distribution to a given final one in a given time at the lowest cost as quantified by total entropy production. We prove that for a system with discrete states this optimal process involves nonconservative driving, i.e., a genuine driving affinity, in contrast to the case of a system with continuous states. In a multicyclic network, the optimal driving affinity is bounded by the number of states within each cycle. If the driving affects forward and backwards rates nonsymmetrically, the bound additionally depends on a structural parameter characterizing this asymmetry.
10 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.
5 citations
TL;DR: In this paper, the authors analyzed the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast and slow driving and showed that in both cases observables can be found that yield an estimate of order one for the total entropy production.
Abstract: The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.
5 citations
TL;DR: In this article, the authors analyzed the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast and slow driving and showed that in both cases observables can be found that yield an estimate of order one for the total entropy production.
Abstract: The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.
1 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
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TL;DR: In this paper, the authors investigated the thermodynamic uncertainty relation of the Kardar-Parisi-Zhang equation on a finite spatial interval and showed that the TUR product displays two distinct regimes which are separated by a critical value of an effective coupling parameter.
Abstract: We investigate the thermodynamic uncertainty relation for the $(1+1)$ dimensional Kardar-Parisi-Zhang 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 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.