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There is a variety of situations in which Newton’s third law is violated. Generally, the action-reaction symmetry can be broken for mesoscopic particles, when their effective interactions are mediated by a nonequilibrium environment. Here, we investigate different classes of nonreciprocal interactions relevant to real experimental situations and present their basic statistical mechanics analysis. We show that in mixtures of particles with such interactions, distinct species acquire distinct kinetic temperatures. In certain cases, the nonreciprocal systems are exactly characterized by a pseudo-Hamiltonian; i.e., being intrinsically nonequilibrium, they can nevertheless be described in terms of equilibrium statistical mechanics. Our results have profound implications, in particular, demonstrating the possibility to generate extreme temperature gradients on the particle scale. We verify the principal theoretical predictions in experimental tests performed with two-dimensional binary complex plasmas.
When a planar bilayer of colloids is exposed to perpendicular flow, the wakes generated downstream from each particle mediate their effective interactions. Most notably, the particle-wake interactions break the action-reaction symmetry for the colloids in different layers. Under quite general conditions we show that, if the interaction nonreciprocity exceeds a certain threshold, this creates an active dispersion of self-propelled particle clusters. The emerging activity promotes unusual melting scenarios and an enormous diffusivity in the dense fluid. Our results are obtained by computer simulation and analytical theory, and can be verified in experiments with colloidal dispersions and complex plasmas.
Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio=reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions.