The local approach to quantum transport may violate the second law of thermodynamics

By Amikam Levy, Ronnie Kosloff. 2014

266 citations recorded by the source corpus.

Clausius statement of the second law of thermodynamics reads: Heat will flow spontaneously from a hot to cold reservoir. This statement should hold for transport of energy through a quantum network composed of small subsystems each coupled to a heat reservoir. When the coupling between nodes is small, it seems reasonable to construct a local master equation for each node in contact with the local reservoir. The energy transport through the network is evaluated by calculating the energy flux after the individual nodes are coupled. We show by analyzing the most simple network composed of two quantum nodes coupled to a hot and cold reservoir, that the local description can result in heat flowing from cold to hot reservoirs, even in the limit of vanishing coupling between the nodes. A global derivation of the master equation which prediagonalizes the total network Hamiltonian and within this framework derives the master equation, is always consistent with the second law of thermodynamics.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/755ce8ceb834342bac850a94d50dcdc7e2bc30f7

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Citations in the corpus

Markovian master equations for quantum thermal machines: local versus global approach (2017, background): “[58, 59, 63], which lack an external field, we find that the presence of such a field ensures that the local master equation does not result in any violations of the laws of thermodynamics.”
Introduction to Quantum Thermodynamics: History and Prospects (2018, background): “What happens when the system can be deconstructed into segments which are weakly coupled to each other? Can one use a local GKLS equation for each segment and then linking together to construct a network? Careful analysis has shown that such a construction can violate the II-law: Heat can flow from ”
Irreversible entropy production: From classical to quantum (2020, background): “(Levy and Kosloff, 2014) it was shown how local master equations seem to violate the second law (allowing, e.g., heat to flow from cold to hot).”
Fundamental aspects of steady-state conversion of heat to work at the nanoscale (2016, background): “[338], which points out that one has to be careful in the treatment of the system if one wants to”
Thermodynamics of quantum systems under dynamical control (2015, background): “In any case, for nanoscale systems totally embedded in thermal baths, such system-bath decoupling may not be possible (Levy and Kosloff, 2014).”
Colloquium : Quantum heat transport in condensed matter systems (2021, background): “…measurement of heat transport in such a circuit addresses some fundamental questions of open quantum systems (Aurell and Montana, 2019; Chiara et al., 2018; Donvil et al., 2020, 2018; Hewgill et al., 2020; Hofer et al., 2017; Levy and Kosloff, 2014; Magazzù and Grifoni, 2019; Rivas et al., 2010).”
Quantum thermodynamics (2015, background): “In [209], the authors discuss how in a network of quantum systems coupled to reservoirs at different temperatures, the second law is violated locally, though its always valid globally, in linewith intuition (see Ref.”
Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures (2015, methodology): “The Lindblad generators are modified accordingly, and heat flows without extracting or consuming work [85].”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “It should be emphasized that in general, the GKLS master equation per se need not obey thermodynamical principles [376, 459], cf.”