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Fluctuation spectra and force generation in nonequilibrium systems

A. Lee,D. Vella,J. Wettlaufer

Published 2015 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

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. 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.

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