Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations.  This phenomenon will be discussed through a simple example of a system in which such correlations are induced by a local drive [1].  In particular it is shown that in two and higher dimensions the presence of a localized drive in an otherwise diffusive system results in steady-state density and current profiles which decay algebraically to their global average value, away from the drive.  The same is true for the density-density correlation function. Close correspondence of these nonequilibrium steady state functions to electrostatic potentials induces by local charge configurations will be pointed out.

1. T. Sadhu, S. Majumdar and D. Mukamel, Phys. Rev. E 84, 051136 (2011); Phys. Rev. E 90,  012109 (2014).