In this paper we report that notions of topological protection can be applied
to stationary configurations that are driven far from equilibrium by active,
dissipative processes. We show this for physically two disparate cases :
stochastic networks governed by microscopic single particle dynamics as well as
collections of driven, interacting particles described by coarse-grained
hydrodynamic theory. In both cases, the presence of dissipative couplings to
the environment that break time reversal symmetry are crucial to ensuring
topologically protection. These examples constitute proof of principle that
notions of topological protection, established in the context of electronic and
mechanical systems, do indeed extend generically to processes that operate out
of equilibrium. Such topologically robust boundary modes have implications for
both biological and synthetic systems.Comment: 11 pages, 4 figures (SI: 8 pages 3 figures
