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Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved July 10, 2017 (received for review January 31, 2017)
Significance
Understanding force generation in nonequilibrium systems is a significant challenge in statistical and biological physics. We show that force generation in nonequilibrium systems is encoded in their energy fluctuation spectra. In particular, a nonequipartition of energy, which is only possible in active systems, can lead to a nonmonotonic fluctuation spectrum. For a narrow, unimodal spectrum, we find that the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. Our results agree with recent molecular dynamics simulations of active Brownian particles, and shed light on the old riddle of the Maritime Casimir effect.
Abstract
Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The nonequilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that, for a narrow, unimodal spectrum, the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important nonequilibrium interactions are encoded within the fluctuation spectrum. In this sense, the noise becomes the signal.
Footnotes
- ↵1To whom correspondence may be addressed. Email: john.wettlaufer{at}yale.edu, alphalee{at}g.harvard.edu, or dominic.vella{at}maths.ox.ac.uk.
Author contributions: A.A.L., D.V., and J.S.W. designed research, performed research, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Nonequilibrium fluctuation spectra and forces
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