We give a sufficient condition under which an applied nonequilibrium driving in a medium always has a stabilizing effect on an attached quasi-static probe. We show that the resulting Lamb shift in the symmetric part of the stiffness matrix with respect to equilibrium is positive and depends strongly on the nonequilibrium density far away from the probe. For illustration we take the example of diffusive medium particles with a self-potential in the shape of a Mexican hat, repulsive at the origin and attractive near the border of a disk where the potential energy gets very large. They undergo a rotational force around the origin. For no or small rotation in the medium, the origin is an unstable fixed point for the probe and the precise shape of the self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain threshold of the rotation amplitude the origin becomes stable for the probe and more details of the medium start to matter.
(Joint work with Urna Basu, Pierre de Buyl and Karel Netocny)
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