TY - JOUR
T1 - Markovian master equations for quantum thermal machines
T2 - Local versus global approach
AU - Hofer, Patrick P.
AU - Perarnau-Llobet, Martí
AU - Miranda, L. David M.
AU - Haack, Géraldine
AU - Silva, Ralph
AU - Brask, Jonatan Bohr
AU - Brunner, Nicolas
PY - 2017/12/1
Y1 - 2017/12/1
N2 - The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.
AB - The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.
KW - exact numerics
KW - heat engine
KW - Markovian master equations
KW - quantum thermodynamics
U2 - 10.1088/1367-2630/aa964f
DO - 10.1088/1367-2630/aa964f
M3 - Article
AN - SCOPUS:85039792665
SN - 1367-2630
VL - 19
JO - New Journal of Physics
JF - New Journal of Physics
IS - 12
M1 - 123037
ER -