{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T01:16:41Z","timestamp":1773278201110,"version":"3.50.1"},"reference-count":46,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p> When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added \u2018by hand\u2019. Although simple, the resulting local master equation (LME) is known to be thermodynamically inconsistent. Otherwise, one may always obtain a consistent global master equation (GME) by working on the energy basis of the full interacting Hamiltonian. Here, we consider a two-node \u2018quantum wire\u2019 connected to two heat baths. The stationary solution of the LME and GME are obtained and benchmarked against the exact result. Importantly, in our model, the validity of the GME is constrained by the underlying secular approximation. Whenever this breaks down (for resonant weakly-coupled nodes), we observe that the LME, in spite of being thermodynamically flawed: (a) predicts the correct steady state, (b) yields with the exact asymptotic heat currents, and (c) reliably reflects the correlations between the nodes. In contrast, the GME fails at all three tasks. Nonetheless, as the inter-node coupling grows, the LME breaks down whilst the GME becomes correct. Hence, the global and local approach may be viewed as complementary tools, best suited to different parameter regimes. <\/jats:p>","DOI":"10.1142\/s1230161217400108","type":"journal-article","created":{"date-parts":[[2017,12,17]],"date-time":"2017-12-17T22:56:39Z","timestamp":1513551399000},"page":"1740010","source":"Crossref","is-referenced-by-count":158,"title":["Testing the Validity of the \u2018Local\u2019 and \u2018Global\u2019 GKLS Master Equations on an Exactly Solvable Model"],"prefix":"10.1142","volume":"24","author":[{"given":"J. Onam","family":"Gonz\u00e1lez","sequence":"first","affiliation":[{"name":"Dpto. de F\u00edsica and IUdEA: Instituto Universitario de Estudios Avanzados Universidad de La Laguna, 38203, Spain"},{"name":"School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom"}]},{"given":"Luis A.","family":"Correa","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom"}]},{"given":"Giorgio","family":"Nocerino","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom"}]},{"given":"Jos\u00e9 P.","family":"Palao","sequence":"additional","affiliation":[{"name":"Dpto. de F\u00edsica and IUdEA: Instituto Universitario de Estudios Avanzados Universidad de La Laguna, 38203, Spain"}]},{"given":"Daniel","family":"Alonso","sequence":"additional","affiliation":[{"name":"Dpto. de F\u00edsica and IUdEA: Instituto Universitario de Estudios Avanzados Universidad de La Laguna, 38203, Spain"}]},{"given":"Gerardo","family":"Adesso","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, University Park, Nottingham NG7 2RD, United 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