Abstract
Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealized work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly.
- Received 26 April 2019
- Revised 14 August 2019
DOI:https://doi.org/10.1103/PhysRevX.9.041032
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
About 200 years ago, the invention of equilibrium thermodynamics as a versatile theoretical toolbox was largely driven by the quest to design powerful and efficient heat engines. Today, a similarly versatile nonequilibrium thermodynamic theory for active matter systems, which comprise many self-driven particles, remains elusive. When operating with active matter, radically different engine designs are possible. For example, asymmetrically shaped obstacles immersed in active matter have been shown to move persistently, which in equilibrium would be prohibited by the second law of thermodynamics. This motion is sufficient to drive a simple autonomous engine. We have developed a general thermodynamic framework that allows us to characterize the power and efficiency of such engines from the point of view of a macroscopic observer.
The optimization of engine power and efficiency reveals fundamental design principles. Strikingly, a kite-shaped obstacle with little “wings” performs significantly better than other, highly idealized, engines. Moreover, we show that, as a collective effect, an engine is much more efficient when driven by many active particles than by just one. Extensive numerical simulations confirm these analytical predictions.
Starting with simple toy models, we obtain universal benchmarks for the extraction of work from active matter. It will be interesting to see how well more elaborate theoretical models and experimental realizations of engines perform with respect to these benchmarks.
