GS acknowledges support from the EU FP7 projects FP7 People 2009 IRSES 247007 CACOMEL and FP7 People 2013 IRSES 612285 CANTOR. This work was also supported by the National Academy of Sciences of Belarus through the program 'Convergence', by the External Fellowship Program of the Russian Quantum Center at Skolkovo (D M, S K and E G) and by FAPESP grant 2014/21188-0 (D M), NK and DM acknowledge the support provided by the Scottish Universities Physics Alliance (SUPA). The research leading to these results has received funding from the European Community Seventh Framework Programme (FP7/2007-2013) under grant agreement n. 270843 (iQIT) Date of acceptance: 31/03/2015 We present a one-dimensional tight-binding chain of two-level systems coupled only through common dissipative Markovian reservoirs. This quantum chain can demonstrate anomalous thermodynamic behavior contradicting Fourier law. Population dynamics of individual systems of the chain is polynomial with the order determined by the initial state of the chain. The chain can simulate classically hard problems, such as multi-dimensional random walks. Publisher PDF
