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  • 1. Argun, Aykut
    et al.
    Soni, Jalpa
    Dabelow, Lennart
    Bo, Stefano
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Pesce, Giuseppe
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Volpe, Giovanni
    Experimental realization of a minimal microscopic heat engine2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 5, article id 052106Article in journal (Refereed)
    Abstract [en]

    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.

  • 2. Aristov, Maria
    et al.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Bechinger, Clemens
    Separation of chiral colloidal particles in a helical flow field2013In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 9, no 8, p. 2525-2530Article in journal (Refereed)
    Abstract [en]

    Stereoisomeric molecules with opposite chirality, so-called enantiomers, often vary regarding their sensory, pharmacological and toxicological properties. Such enantiomer specific effects play a central role in the development, testing and evaluation of drugs, pesticides and food related products. Accordingly, efficient techniques for separation of chiral mixtures into enantiopure compounds are of enormous practical relevance. Most current enantiomer separation methods are based on enantioselective interactions with an auxiliary substance which has to be developed and optimized for different chiral molecules in an elaborate and costly process. Here, we experimentally demonstrate the separation of micron-sized chiral particles in a helical fluid flow which is created inside a microfluidic device patterned with slanted grooves. We observe that the retention time of particles in a helical flow field strongly depends on their chirality which leads to an effective chiral separation within the channel. Our experimental results are confirmed by numerical calculations which demonstrate how the coupling of rotational and translational degrees of freedom leads to differences in the trajectories of particles with opposite chirality. Since our separation mechanism does not rely on material specific interactions, this offers considerable advantages over existing methods. We expect that our approach can be also applied at nanometre length scales by using channels with smaller diameters and with an optimized geometry.

  • 3. Aurell, Erik
    et al.
    Bo, Stefano
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Dias, Marcelo
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Aalto University, Finland.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Marino, Raffaele
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Diffusion of a Brownian ellipsoid in a force field2016In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 114, no 3, article id 30005Article in journal (Refereed)
    Abstract [en]

    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.

  • 4. Aurell, Erik
    et al.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    On the von Neumann entropy of a bath linearly coupled to a driven quantum system2015In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 17, article id 065007Article in journal (Refereed)
    Abstract [en]

    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(B)T, and the second and the third other functionals which have no analogue in stochastic thermodynamics.

  • 5. Behringer, Hans
    et al.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brownian dynamics simulations with hard-body interactions: Spherical particles2012In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 137, no 16, p. 164108-Article in journal (Refereed)
    Abstract [en]

    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.

  • 6.
    Bo, Stefano
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Driven Anisotropic Diffusion at Boundaries: Noise Rectification and Particle Sorting2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 119, no 6, article id 060603Article in journal (Refereed)
    Abstract [en]

    We study the diffusive dynamics of a Brownian particle in the proximity of a flat surface under nonequilibrium 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 setup to observe this novel noise-induced transport mechanism. We furthermore show that it is sensitive to particle characteristics, such that this setup can be used for sorting particles of different sizes.

  • 7.
    Bo, Stefano
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Lim, Soon Hoe
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Functionals in stochastic thermodynamics: how to interpret stochastic integrals2019In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 084005Article in journal (Refereed)
    Abstract [en]

    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.

  • 8.
    Bo, Stefano
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Schmidt, Falko
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Volpe, Giovanni
    Measurement of anomalous diffusion using recurrent neural networks2019In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 100, no 1, article id 010102Article in journal (Refereed)
    Abstract [en]

    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 (RNNs) 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 RNNs 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 subdiffusive colloids trapped in speckle light fields and superdiffusive microswimmers.

  • 9. Bogunovic, Lukas
    et al.
    Fliedner, Marc
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Wegener, Sonja
    Regtmeier, Jan
    Anselmetti, Dario
    Reimann, Peter
    Chiral Particle Separation by a Nonchiral Microlattice2012In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 109, no 10, p. 100603-Article in journal (Refereed)
    Abstract [en]

    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: Microparticles 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 relative to the fluid flow.

  • 10. Celani, Antonio
    et al.
    Bo, Stefano
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Aurell, Erik
    Anomalous Thermodynamics at the Microscale2012In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 109, no 26, p. 260603-Article in journal (Refereed)
    Abstract [en]

    Particle motion at the microscale 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 to this result, here we show that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment are considered, in the 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, which we call an entropic anomaly, is due to a symmetry breaking that occurs when moving to the small, finite inertia limit. Anomalous entropy production is traced back to futile phase-space cyclic trajectories displaying a fast downgradient sweep followed by a slow upgradient return to the original position. DOI: 10.1103/PhysRevLett.109.260603

  • 11. Dabelow, Lennart
    et al.
    Bo, Stefano
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Irreversibility in Active Matter Systems: Fluctuation Theorem and Mutual Information2019In: Physical Review X, ISSN 2160-3308, E-ISSN 2160-3308, Vol. 9, no 2, article id 021009Article in journal (Refereed)
    Abstract [en]

    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 nonequilibrium 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 nonequilibrium environment. The resulting irreversibility measure fulfills an integral fluctuation theorem and a secondlaw-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.

  • 12. Helden, Laurent
    et al.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Bechinger, Clemens
    Direct measurement of thermophoretic forces2015In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 11, no 12, p. 2379-2386Article in journal (Refereed)
    Abstract [en]

    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 ST(T) is determined for r = 2.5 mm polystyrene and r = 1.35 mm melamine particles. The functional form of ST(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.

  • 13. Kuemmel, Felix
    et al.
    ten Hagen, Borge
    Wittkowski, Raphael
    Buttinoni, Ivo
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Volpe, Giovanni
    Loewen, Hartmut
    Bechinger, Clemens
    Circular Motion of Asymmetric Self-Propelling Particles2013In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 110, no 19, p. 198302-Article in journal (Refereed)
    Abstract [en]

    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.

  • 14.
    Manikandan, Sreekanth K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Dabelow, Lennart
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Krishnamurthy, Supriya
    Stockholm University, Faculty of Science, Department of Physics.
    Efficiency Fluctuations in Microscopic Machines2019In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, no 14, article id 140601Article in journal (Refereed)
    Abstract [en]

    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 by Verley et al. [Nat. Commun. 5, 4721 (2014); Phys. Rev. E 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 nontrivial models of colloidal engines.

  • 15. Marichez, Vincent
    et al.
    Tassoni, Alessandra
    Cameron, Robert P.
    Barnett, Stephen M.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Genet, Cyriaque
    Hermans, Thomas M.
    Mechanical chiral resolution2019In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 15, no 23, p. 4593-4608Article, review/survey (Refereed)
    Abstract [en]

    Mechanical interactions of chiral objects with their environment are well-established at the macroscale, like a propeller on a plane or a rudder on a boat. At the colloidal scale and smaller, however, such interactions are often not considered or deemed irrelevant due to Brownian motion. As we will show in this tutorial review, mechanical interactions do have significant effects on chiral objects at all scales, and can be induced using shearing surfaces, collisions with walls or repetitive microstructures, fluid flows, or by applying electrical or optical forces. Achieving chiral resolution by mechanical means is very promising in the field of soft matter and to industry, but has not received much attention so far.

  • 16.
    Marino, Raffaele
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Aurell, Erik
    Entropy production of a Brownian ellipsoid in the overdamped limit2016In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 93, no 1, article id 012132Article in journal (Refereed)
    Abstract [en]

    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.

  • 17. Viefhues, Martina
    et al.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    DNA dielectrophoresis: Theory and applications a review2017In: Electrophoresis, ISSN 0173-0835, E-ISSN 1522-2683, Vol. 38, no 11, p. 1483-1506Article, review/survey (Refereed)
    Abstract [en]

    Dielectrophoresis is the migration of an electrically polarizable particle in an inhomogeneous electric field. This migration can be exploited for several applications with (bio)molecules or cells. Dielectrophoresis is a noninvasive technique; therefore, it is very convenient for (selective) manipulation of (bio)molecules or cells. In this review, we will focus on DNA dielectrophoresis as this technique offers several advantages in trapping and immobilization, separation and purification, and analysis of DNA molecules. We present and discuss the underlying theory of the most important forces that have to be considered for applications with dielectrophoresis. Moreover, a review of DNA dielectrophoresis applications is provided to present the state-of-the-art and to offer the reader a perspective of the advances and current limitations of DNA dielectrophoresis.

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