Rate of Entropy Production in Stochastic Mechanical Systems

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems.

Investigation of Micro-volume Viscosity with Janus Microbeads Based on Rotational Brownian Motion

Viscosity is an important property of liquids. A viscosity change of aqueous substances that deviates from their normal levels usually implies a compromise in quality due to degradation or microorganism proliferation. Monitoring of macro-scale viscosity can be simply realized by various conventional tools, such as rotational viscometers, capillary tubes, falling bodies, and so forth. Nevertheless, today, micro-volume viscosity measurement remains a challenging endeavor, resulting in rare, expensive, or difficult-to-obtain samples not very well studied. For this reason, a novel technique for micro-viscosity based on rotational Brownian motion is presented in this paper. Janus microbeads were made by coating fluorescent polystyrene beads with gold film. Taking advantage of the bead configuration of half gold/half fluorescence, the rotational Brownian signal was expressed in terms of blinking fluorescent intensity. The characteristic correlation time was derived from the blinking intensity of trace amounts of a selected medium over a certain time period, and results were correlated with viscosity. Given a volume of only 2 μL for each measurement, calibration of a series of glycerol–water mixtures (100%–1% (v/v) water content) yielded good agreement with the expected viscosity predictions over the range of 0.8–574.8 cP. Five common oil products, including lubricant oil, baby oil, food oil, olive oil, and motor oil, were further investigated to demonstrate the feasibility and practicability of the proposed technique. Data measured by the rotational Brownian motion-based diffusometer were comparable with those measured by a commercial rotational viscometer. The method also explicitly showed viscosity degradation after the oils were heated at a high temperature of over 100 °C for 10 min. Evaluation proved the proposed Janus microbead-enabled rotational diffusometric technique to be a promising approach for rapid and micro-scale viscosity measurement.

Application of the Multi-Particle Collision Dynamics Method to a Suspension of Magnetic Spherical Particles

In order to apply the multi-particle collision dynamics (MPCD) method to a magnetic particle suspension, we have elucidated the dependence of the translational and rotational Brownian motion of magnetic particles on the MPCD parameters that characterize the MPCD simulation method. We here consider a two-dimensional system composed of magnetic spherical particles in thermodynamic equilibrium. The diffuse reflection model has been employed for treating the interactions between fluid and magnetic particles. In the diffuse reflection model, the interactions between fluid and magnetic particles are transferred into the translational motion more strongly than into the rotational motion of magnetic particles. The employment of relatively small simulation time steps gives rise to a satisfactory level of the translational Brownian motion. The activation level of the Brownian motion is almost independent of both the size of the unit collision cell and the number of fluid particles per cell. Larger values of the maximum rotation angle induce stronger translational and rotational Brownian motion, but in the present magnetic particle suspension the range between around π/4 and π/2 seems to be reasonable. We may conclude that the MPCD method with the simple diffuse reflection model is a feasible simulation technique as the first approximation for analyzing the behavior of magnetic particles in a suspension. If more accurate solutions regarding the aggregate structures of magnetic particles are required, the introduction of the scaling coefficient regarding the interactions between fluid and magnetic particles can yield more accurate and physically reasonable aggregate structures in both a qualitative and quantitative meanings.