Search

A microscopic model for a translational Brownian motor, dubbed as Brownian Translator, is introduced. It is inspired by the Brownian Gyrator of Filliger and Reimann (Filliger and Reimann 2007). The Brownian Translator consists of a spatially asymmetric object moving freely along a line due to perpetual collisions with a surrounding ideal gas. When this gas has an anisotropic temperature, both spatial and temporal symmetries are broken and the object acquires a nonzero drift. Onsager reciprocity implies the opposite phenomenon, that is dragging a spatially asymmetric object in an (initially at) equilibrium gas induces an energy flow that results in anisotropic gas temperatures. Expressions for the dynamical and energetic properties are derived as a series expansion in the mass ratio (of gas particle vs. object). These results are in excellent agreement with molecular dynamics simulations., Comment: 20 pages, 6 figures

Active matter describes systems whose constituents convert energy from their surroundings into directed motion, such as bacteria or catalytic colloids. We unravel a remarkable direct link between the dynamics and thermodynamics for suspensions of such active particles: The thermodynamic equivalent of irreversibility is the swim pressure. Like in the famous fluctuation theorems of stochastic thermodynamics, irreversibility is defined as the log-ratio of the probabilities to observe a given set of particle trajectories and their time reverses. Our discovery is thus similar in spirit to what is known for passive systems, for which those fluctuation theorems relate the irreversibility to the thermodynamic entropy. It is based on numerical simulations and on analytical arguments for the limits of low particle density and/or high activity in the paradigmatic model of active Ornstein-Uhlenbeck particles., Comment: 11 pages, 3 figures (+ suppl. 8 pages, 1 figure)

A general formalism is derived describing both dynamical and energetic properties of a microscopic Feynman ratchet. Work and heat flows are given as a series expansion in the thermodynamic forces, obtaining analytical expressions for the (non)linear response coefficients. Our results extend previously obtained expressions in the context of a chiral heat pump., Comment: 12 pages, 1 figure

Inspired by biology, great progress has been made in creating artificial molecular motors. However, the dream of harnessing proteins - the building blocks selected by Nature - to design autonomous motors has so far remained elusive. Here we report the synthesis and characterization of the Lawnmower, an autonomous, protein-based artificial molecular motor comprised of a spherical hub decorated with proteases. Its "burnt-bridge" motion is directed by cleavage of a peptide lawn, promoting motion towards unvisited substrate. We find that Lawnmowers exhibit directional motion with average speeds of up to 80 nm/s, comparable to biological motors. By selectively patterning the peptide lawn on microfabricated tracks, we furthermore show that the Lawnmower is capable of track-guided motion. Our work opens an avenue towards nanotechnology applications of artificial protein motors.

The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g., an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features, in particular in the steady state. We here focus on the time-reversal symmetry of individual spatial trajectories as a distinct equilibrium characteristic. We investigate to what extent the steady-state trajectories of a trapped active particle obey or break this time-reversal symmetry. Within the framework of active Ornstein-Uhlenbeck particles we find that the steady-state trajectories in a harmonic potential fulfill path-wise time-reversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials., Comment: 31 pages, 10 figures

Active matter systems are driven out of equilibrium by conversion of energy into directed motion locally on the level of the individual constituents. In the spirit of a minimal description, active matter is often modeled by so-called active Ornstein-Uhlenbeck particles (AOUPs), an extension of passive Brownian motion where activity is represented by an additional fluctuating non-equilibrium "force" with simple statistical properties (Ornstein-Uhlenbeck process). While in passive Brownian motion, entropy production along trajectories is well-known to relate to irreversibility in terms of the log-ratio of probabilities to observe a certain particle trajectory forward in time in comparison to observing its time-reversed twin trajectory, the connection between these concepts for active matter is less clear. It is therefore of central importance to provide explicit expressions for the irreversibility of active particle trajectories based on measurable quantities alone, such as the particle positions. In this technical note, we derive a general expression for the irreversibility of AOUPs in terms of path probability ratios (forward versus backward path), extending recent results from [PRX 9, 021009 (2019)] by allowing for arbitrary initial particle distributions and states of the active driving., Comment: 14 pages

In stochastic thermodynamics standard concepts from macroscopic thermodynamics, such as heat, work, and entropy production, are generalized to small fluctuating systems by defining them on a trajectory-wise level. In Langevin systems with continuous state-space such definitions involve stochastic integrals along system trajectories, whose specific values depend on the discretization rule used to evaluate them (i.e. the "interpretation" of the noise terms in the integral). Via a systematic mathematical investigation of this apparent dilemma, we corroborate the widely used standard interpretation of heat- and work-like functionals as Stratonovich integrals. We furthermore recapitulate the anomalies that are known to occur for entropy production in the presence of temperature gradients., Comment: 29 pages, accepted for publication in the Journal of Statistical Mechanics: theory and experiment

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently characterize anomalous diffusion by determining the exponent from a single short trajectory, outperforming the standard estimation based on the MSD when the available data points are limited, as is often the case in experiments. Furthermore, the RNN can handle more complex tasks where there are no standard approaches, such as determining the anomalous diffusion exponent from a trajectory sampled at irregular times, and estimating the switching time and anomalous diffusion exponents of an intermittent system that switches between different kinds of anomalous diffusion. We validate our method on experimental data obtained from sub-diffusive colloids trapped in speckle light fields and super-diffusive microswimmers., Comment: 6 pages, 4 figures. Supplemental material available as separate file in the Ancillary Files section

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a `universal theory of efficiency fluctuations' at long times, for machines with a finite state space, was developed in [Verley \textit{et al.}, Nat.~Commun.~\textbf{5}, 4721 (2014); Phys.~Rev.~E~\textbf{90}, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the `universal features' and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two non-trivial models of colloidal engines., Comment: 12 pages, 6 Figures; version published in the journal

We consider a Brownian particle which, in addition to being in contact with a thermal bath, is driven by fluctuating forces which stem from active processes in the system, such as self-propulsion or collisions with other active particles. These active fluctuations do not fulfill a fluctuation-dissipation relation and therefore play the role of a non-equilibrium environment, which keeps the system permanently out of thermal equilibrium even in the absence of external forces. We investigate how the out-of-equilibrium character of the active matter system and the associated irreversibility is reflected in the trajectories of the Brownian particle. Specifically, we analyze the log-ratio of path probabilities for observing a certain particle trajectory forward in time versus observing its time-reversed twin trajectory. For passive Brownian motion, it is well-known that this path probability ratio quantifies irreversibility in terms of entropy production. For active Brownian motion, we show that in addition to the usual entropy produced in the thermal environment the path probability ratio contains a contribution to irreversibility from mutual information production between the particle trajectory and the history of the non-equilibrium environment. The resulting irreversibility measure fulfills an integral fluctuation theorem and a second-law like relation. When deriving and discussing these relations, we keep in mind that the active fluctuations can occur either due to a suspension of active particles pushing around a passive colloid or due to active self-propulsion of the particle itself; we point out the similarities and differences between these two situations. We obtain explicit expressions for active fluctuations modeled by an Ornstein-Uhlenbeck process. Finally, we illustrate our general results by analyzing a Brownian particle which is trapped in a static or moving harmonic potential., Comment: 31 pages, 4 figures

Microscopic heat engines are microscale systems that convert energy flows between heat reservoirs into work or systematic motion. We have experimentally realized a minimal microscopic heat engine. It consists of a colloidal Brownian particle optically trapped in an elliptical potential well and simultaneously coupled to two heat baths at different temperatures acting along perpendicular directions. For a generic arrangement of the principal directions of the baths and the potential, the symmetry of the system is broken, such that the heat flow drives a systematic gyrating motion of the particle around the potential minimum. Using the experimentally measured trajectories, we quantify the gyrating motion of the particle, the resulting torque that it exerts on the potential, and the associated heat flow between the heat baths. We find excellent agreement between the experimental results and the theoretical predictions., Comment: 8 pages, 5 figures

We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial directions. By presenting the exact time-dependent solution of the Fokker-Planck equation for this problem, we demonstrate that the interplay between anisotropic diffusion and hard-core interaction with the plain wall rectifies the thermal fluctuations and induces directed particle transport parallel to the surface, without any deterministic forces being applied in that direction. Based on current micromanipulation technologies, we suggest a concrete experimental set-up to observe this novel noise-induced transport mechanism. We furthermore show that it is sensitive to particle characteristics, such that this set-up can be used for sorting particles of different size., Comment: 6 pages, 1 figure. Supplemental Material provided as a separate pdf file, see ancillary file

We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles., Comment: 17 pages, 1 fig

The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman-Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman-Vernon theory. In the classical limit of Kramers-Langevin dynamics (Caldeira-Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of $k_BT$, the second another functional with no analogue in stochastic thermodynamics, and the third is a boundary term., Comment: 10 pages, no figures

We study the thermophoretic motion of a micron sized single colloidal particle in front of a flat wall by evanescent light scattering. To quantify thermophoretic effects we analyse the nonequilibrium steady state (NESS) of the particle in a constant temperature gradient perpendicular to the confining walls. We propose to determine thermophoretic forces from a 'generalized potential' associated with the probability distribution of the particle position in the NESS. Experimentally we demonstrate, how this spatial probability distribution is measured and how thermophoretic forces can be extracted with 10 fN resolution. By varying temperature gradient and ambient temperature, the temperature dependence of Soret coefficient $S_T(T)$ is determined for $r = 2.5 \mu m$ polystyrene and $r = 1.35 \mu m$ melamine particles. The functional form of $S_T(T)$ is in good agreement with findings for smaller colloids. In addition, we measure and discuss hydrodynamic effects in the confined geometry. The theoretical and experimental technique proposed here extends thermophoresis measurements to so far inaccessible particle sizes and particle solvent combinations.

The superconducting RF linac for LCLS-II calls for 1.3 GHz 9-cell cavities with an average intrinsic quality factor Q0 of 2.7x10^10 at 2 K and 16 MV/m accelerating gradient. Two niobium 9-cell cavities, prepared with nitrogen-doping at Fermilab, were assembled into the Cornell Horizontal Test Cryomodule (HTC) to test cavity performance in a cryomodule that is very similar to a full LCLS-II cryomodule. The cavities met LCLS-II specifications with an average quench field of 17 MV/m and an average Q0 of 3x10^10. The sensitivity of the cavities' residual resistance to ambient magnetic field was determined to be 0.5 nOhm/mG during fast cool down. In two cool downs, a heater attached to one of the cavity beam tubes was used to induce large horizontal temperature gradients. Here we report on the results of these first tests of nitrogen-doped cavities in cryomodule, which provide critical information for the LCLS-II project., Comment: 11 pages, 22 figures

In a Comment [Phys. Rev. Lett. 113, 029801 (2014)] on our Letter on self-propelled asymmetric particles [Phys. Rev. Lett. 110, 198302 (2013); arXiv:1302.5787], Felderhof claims that our theory based on Langevin equations would be conceptually wrong. In this Reply we show that our theory is appropriate, consistent, and physically justified., Comment: 2 pages

The dependence of the Q-value on the RF field (Q-slope) is actively studied in various accelerator laboratories. Although remedies against this dependence have been found, the physical cause still remains obscure. A rather straightforward two-fluid model description of the Q-slope in the low and high field domains is presented with emphasis on the recently experimentally identified improvement of the Q-value by so-called "N-doping".

We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it has been recently shown that a space dependent temperature breaks the time reversal symmetry of the fast velocity degrees of freedom resulting in an anomalous contribution to the entropy production of the overdamped dynamics. We show that optimization of entropy production is determined by an auxiliary deterministic problem describing motion on a curved manifold in a potential. The "anomalous contribution" to entropy plays the role of the potential and the inverse of the diffusion tensor is the metric. We also find that entropy production is not minimized by adiabatically slow, quasi-static protocols but there is a finite optimal duration for the transport process. As an example we discuss the case of a linearly space dependent diffusion coefficient., Comment: 6 pages, 2 figures

Micron-sized self-propelled (active) particles can be considered as model systems for characterizing more complex biological organisms like swimming bacteria or motile cells. We produce asymmetric microswimmers by soft lithography and study their circular motion on a substrate and near channel boundaries. Our experimental observations are in full agreement with a theory of Brownian dynamics for asymmetric self-propelled particles, which couples their translational and orientational motion., Comment: 5 pages, 4 figures, 1 table, accepted for publication in Phys. Rev. Lett

A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the affected component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heuristic algorithms is carried out., Comment: 17 pages

We conceived a model experiment for a continuous separation strategy of chiral molecules (enantiomers) without the need of any chiral selector structure or derivatization agents: Micro-particles that only differ by their chirality are shown to migrate along different directions when driven by a steady fluid flow through a square lattice of cylindrical posts. In accordance with our numerical predictions, the transport directions of the enantiomers depend very sensitively on the orientation of the lattice relatively to the fluid flow.

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a non-convex interaction potential of the two particles.

Particle motion at the micro-scale is an incessant tug-of-war between thermal fluctuations and applied forces on one side, and the strong resistance exerted by fluid viscosity on the other. Friction is so strong that completely neglecting inertia - the overdamped approximation - gives an excellent effective description of the actual particle mechanics. In sharp contrast with this result, here we show that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment is considered, in presence of temperature gradients. In the limit of vanishingly small, yet finite inertia, we find that the entropy production is dominated by a contribution that is anomalous, i.e. has no counterpart in the overdamped approximation. This phenomenon, that we call entropic anomaly, is due to a symmetry-breaking that occurs when moving to the small, finite inertia limit. Strong production of anomalous entropy is traced back to intense sweeps down the temperature gradient., Comment: 4 pages, 1 figure, supplementary information uploaded as a separate pdf file (see other formats link)

We propose a method to separate enantiomers in microfluidic or nanofluidic channels. It requires flow profiles which break chiral symmetry and have regions with high local shear. Such profiles can be generated in channels confined by walls with different hydrodynamic boundary conditions (e.g. slip lengths). Due to a nonlinear hydrodynamic effect, particles with different chirality migrate at different speed and can be separated. The mechanism is demonstrated by computer simulations. We investigate the influence of thermal fluctuations (i.e. the P\'eclet number) and show that the effect disappears in the linear response regime. The details of the microscopic flow are important and determine which volume forces are necessary to achieve separation., Comment: Accepted for publication in Physical Review Letters

We theoretically predict and experimentally demonstrate that several different particle species can be separated from each other by means of a ratchet device, consisting of periodically arranged triangular (ratchet) shaped obstacles. We propose an explicit algorithm for suitably tailoring the externally applied, time-dependent voltage protocol so that one or several, arbitrarily selected particle species are forced to migrate oppositely to all the remaining species. As an example we present numerical simulations for a mixture of five species, labelled according to their increasing size, so that species 2 and 4 simultaneously move in one direction and species 1, 3, and 5 in the other. The selection of species to be separated from the others can be changed at any time by simply adapting the voltage protocol. This general theoretical concept to utilize one device for many different sorting tasks is experimentally confirmed for a mixture of three colloidal particle species.

The unbiased thermal diffusion of an overdamped Brownian particle in a square lattice potential is considered in the presence of an externally applied ac driving. The resulting diffusion matrix exhibits two orthogonal eigenvectors with eigenvalues $D_1>D_2>0$, indicating anisotropic diffusion along a "fast" and a "slow principal axis". For sufficiently small temperatures, $D_1$ may become arbitrarily large and at the same time $D_2$ arbitrarily small. The principal diffusion axis can be made to point into (almost) any direction by varying either the driving amplitude or the coupling of the particle to the potential, without changing any other property of the system or the driving., Comment: 7 pages, 7 figures

Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions., Comment: 4 pages, 4 figures

The diffusion of an overdamped Brownian particle in a tilted periodic potential is known to exhibit a pronounced enhancement over the free thermal diffusion within a small interval of tilt-values. Here we show that weak disorder in the form of small, time-independent deviations from a strictly spatially periodic potential may further boost this diffusion peak by orders of magnitude. Our general theoretical predictions are in excellent agreement with experimental observations., Comment: Phys. Rev. Lett., in press

We consider a Brownian particle in a ``meandering'' periodic potential when the ambient temperature is a periodically or stochastically varying function of time. Though far from equilibrium, the linear response of the particle to an external static force is exactly the same as in the equilibrium case, i.e. for constant temperature. Even more surprising is the non-linear response: the particle slows down and then even starts to move in the direction opposite to the applied force., Comment: 4 pages, 5 figures

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility)., Comment: 4 pages, 3 figures, to be published in PRL