Using the framework of stochastic thermodynamics, we present an experimental study of a doublet of magnetic colloidal particles that is manipulated by a time-dependent magnetic field. Because of hydrodynamic interactions, each bead experiences a state-dependent friction, which we characterize using a hydrodynamic model. In this work, we compare two estimates of the dissipation in this system: the first one is energy based since it relies on the measured interaction potential, while the second one is information based since it uses only the information content of the trajectories. While the latter only offers a lower bound of the former, we find it to be simple to implement and of general applicability to more complex systems. DOI: 10.1103/PhysRevLett.112.180604 PACS numbers: 05.20.Jj, 05.40.Ca, 05.70.Ln, 82.70.Dd In the last decade, a broad number of works have significantly improved our understanding of the thermodynamics of small systems. A central idea, namely the application of thermodynamics at the level of trajectories, has developed into a field of its own now called stochastic thermodynamics [1][2][3][4]. Manipulated colloids are a paradigmatic example of stochastic thermodynamics because of the ease with which colloids can be manipulated and observed.Many studies of such systems have used a single colloidal particle, in a harmonic [5] or anharmonic potential [3,6], which is described by an overdamped Langevin equation with a constant diffusion coefficient. Recently, Celani et al. have pointed out that the overdamped Langevin description fails to capture some aspects of the thermodynamics of this system in the presence of multiplicative noise due to temperature gradients [7]. In soft matter systems, temperature gradients are difficult to control at the micron scale, but multiplicative noise arises frequently due to hydrodynamic friction. In this Letter, we study such a case using a pair of magnetic colloids that are manipulated by a time-dependent magnetic field. This system offers a convenient mean to measure forces in various soft matter and biological systems because the colloids can be embedded in complex fluids or molecules of interest can be grafted on them [8].In this Letter, we focus on a pair of bare manipulated colloids in water. In the first part, we evaluate the work distribution in this system within stochastic thermodynamics. In the second part, we evaluate an information theoretic bound for the dissipation in this process using only trajectory information.The projection of the Brownian motion of both beads is observed in the plane parallel to the bottom wall with video microscopy. We assume that the fluctuations perpendicular to the wall are negligible since the beads have settled under gravity. Therefore, we focus on the two-dimensional relative displacement vector in polar coordinates r ¼ ðr; θÞ, as shown in Fig. 1.The interaction between the beads is modeled using a potential, which is the sum of three contributions: the dipolar interaction of the magnetic beads with each other U di...
Red blood cells under shear flow present a specific swinging motion superimposed to a fluidlike tanktreading motion. Swinging is hypothesized to originate from periodic storage of shear energy in the cell membrane. Here we designed giant unilamellar vesicles with two lipid phases separated by a contact line, which swing and tanktread like red cells. We propose a model that quantitatively fits our data, finds the value of the contact-line tension and shows that swinging is due to the storage of elastic energy associated with the periodic modulation of the contact-line length during tanktreading. I.
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