Rivas, ÁngelMartín-Delgado Alcántara, Miguel Ángel2023-06-172023-06-172017-07-252045-232210.1038/s41598-017-06722-xhttps://hdl.handle.net/20.500.14352/18165© 2017 the autors and Macmillan Publishers Limited, part of Springer Nature. We acknowledge the Spanish MINECO grants FIS2015-67411, FIS2012-33152, and a “Juan de la Cierva Incorporación” research contract, the CAM research consortium QUITEMAD+ S2013/ICE-2801, and U.S. Army Research Ofce through grant W911NF-14-1-0103 for partial fnancial support.The study of non-equilibrium properties in topological systems is of practical and fundamental importance. Here, we analyze the stationary properties of a two-dimensional bosonic Hofstadter lattice coupled to two thermal baths in the quantum open-system formalism. Novel phenomena appear like chiral edge heat currents that are the out-of-equilibrium counterparts of the zero-temperature edge currents. They support a new concept of dissipative symmetry-protection, where a set of discrete symmetries protects topological heat currents, difering from the symmetry-protection devised in closed systems and zero-temperature. Remarkably, one of these currents fows opposite to the decreasing external temperature gradient. As the starting point, we consider the case of a single external reservoir already showing prominent results like thermal erasure efects and topological thermal currents. Our results are experimentally accessible with platforms like photonics systems and optical lattices.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttp://dx.doi.org/10.1038/s41598-017-06722-xhttps://www.nature.comopen access53Markovian master-equatinsMagnetic-fieldsEdge statesInsulatorsPhotonics.Física-Modelos matemáticos