Showing papers by "Udo Seifert published in 2009"
TL;DR: For soft matter systems strongly driven by stationary flow, an extended fluctuation-dissipation theorem (FDT) is discussed, suggesting an extension of Onsager's regression principle to nonequilibrium steady states.
Abstract: For soft matter systems strongly driven by stationary flow, we discuss an extended fluctuation-dissipation theorem (FDT). Beyond the linear-response regime, the FDT for the stress acquires an additional contribution involving the observable that is conjugate to the strain rate with respect to the dissipation function. This extended FDT is evaluated both analytically for Rouse polymers and in numerical simulations for colloidal suspensions. More generally, our results suggest an extension of Onsager's regression principle to nonequilibrium steady states.
56 citations
TL;DR: This paper integrates the equations of motion in the quasi-spherical limit analytically for time-constant and time-dependent shear flow using matched asymptotic expansions and derives expressions for the amplitude and width of the resonance peaks as a function of the modulation frequency.
Abstract: We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent behaviour, have been identified using numerical methods. In this paper, we integrate the equations of motion in the quasi-spherical limit analytically for time-constant and time-dependent shear flow using matched asymptotic expansions. Using this method, we find analytical expressions for the mean tumbling rate in general time-dependent shear flow. The capsule dynamics is studied in more detail when the inverse shear rate is harmonically modulated around a constant mean value for which a dynamic phase diagram is constructed. By a judicious choice of both modulation frequency and phase, tumbling motion can be induced even if the mean shear rate corresponds to the swinging regime. We derive expressions for the amplitude and width of the resonance peaks as a function of the modulation frequency.
35 citations
TL;DR: In this article, it was shown that for systems with a genuine equilibrium state, the fluctuation-dissipation theorem differs from its equilibrium form by an additive term involving the total entropy production.
Abstract: In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to \emph{energy}. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to \emph{entropy}. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving \emph{total} entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The \emph{a priori} surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.
31 citations
TL;DR: The optimal potential for different temperature profiles is calculated and it is shown that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures, the optimal potential leads to a divergent current.
Abstract: In a spatially periodic temperature profile, directed transport of an overdamped Brownian particle can be induced along a periodic potential. With a load force applied to the particle, this setup can perform as a heat engine. For a given load, the optimal potential maximizes the current and thus the power output of the heat engine. We calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures, the optimal potential leads to a divergent current. This divergence, being an effect of both the overdamped limit and the infinite temperature gradient at the interface, would be cut off in any real experiment.
24 citations
TL;DR: In this article, it was shown that for a two-level spin system, the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.
Abstract: For systems in an externally controllable time dependent potential, the optimal protocol minimizes the mean work spent in a finite time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrodinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations for the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.
19 citations
TL;DR: In this article, the authors show that for a two-level spin system, the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.
Abstract: For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schr\"odinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations of the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.
9 citations
Posted Content•
31 Jul 2009
TL;DR: In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate with respect to energy.
Abstract: In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to \emph{energy} For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to \emph{entropy} By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving \emph{total} entropy production A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems The \emph{a priori} surprising freedom apparently involved in different forms of the FDT in a NESS is clarified
2 citations
TL;DR: In this paper, it was shown that the classical Langevin dynamics for a charged particle on a closed curved surface in a time-independent magnetic field leads to the canonical distribution in the long time limit.
Abstract: We show that the classical Langevin dynamics for a charged particle on a closed curved surface in a time-independent magnetic field leads to the canonical distribution in the long time limit. Thus the Bohr-van Leeuwen theorem holds even for a finite system without any boundary and the average magnetic moment is zero. This is contrary to the recent claim by Kumar and Kumar (EPL, {\bf 86} (2009) 17001), obtained from numerical analysis of Langevin dynamics, that a classical charged particle on the surface of a sphere in the presence of a magnetic field has a nonzero average diamagnetic moment. We extend our analysis to a many-particle system on a curved surface and show that the nonequilibrium fluctuation theorems also hold in this geometry.